Download the source code from here (Get Current Location Using Background Service)
AndroidManifest.xml
<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="servicetutorial.service">
    <uses-permission android:name="android.permission.INTERNET"></uses-permission>
    <uses-permission android:name="android.permission.ACCESS_COARSE_LOCATION"></uses-permission>
    <uses-permission android:name="android.permission.ACCESS_FINE_LOCATION"></uses-permission>
    <application
        android:allowBackup="true"
        android:icon="@mipmap/ic_launcher"
        android:label="@string/app_name"
        android:supportsRtl="true"
        android:theme="@style/AppTheme">
        <activity android:name=".MainActivity"
            android:theme="@android:style/Theme.Translucent.NoTitleBar">
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />
                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
        <service android:name=".GoogleService"></service>
    </application>
</manifest>
activity_main.xml
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:background="#ffffff"
    android:layout_height="match_parent">
    <TextView
        android:layout_width="match_parent"
        android:layout_height="50dp"
        android:background="#3F51B5"
        android:text="Location using service"
        android:textColor="#ffffff"
        android:textSize="20dp"
        android:gravity="center"/>
    <LinearLayout
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:layout_centerInParent="true"
        android:orientation="vertical">
    <LinearLayout
        android:layout_width="match_parent"
        android:orientation="horizontal"
        android:layout_height="50dp">
        <TextView
            android:layout_width="150dp"
            android:layout_height="wrap_content"
            android:text="Latitude"
            android:layout_gravity="center_vertical"
            android:layout_marginLeft="10dp"
            android:textColor="#000000"
            android:textSize="20dp"/>
        <TextView
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:text=""
            android:id="@+id/tv_latitude"
            android:layout_gravity="center_vertical"
            android:layout_marginLeft="10dp"
            android:textColor="#000000"
            android:textSize="20dp"/>
    </LinearLayout>
        <LinearLayout
            android:layout_width="match_parent"
            android:orientation="horizontal"
            android:layout_height="50dp">
            <TextView
                android:layout_width="150dp"
                android:layout_height="wrap_content"
                android:text="Longitude"
                android:layout_gravity="center_vertical"
                android:layout_marginLeft="10dp"
                android:textColor="#000000"
                android:textSize="20dp"/>
            <TextView
                android:layout_width="wrap_content"
                android:layout_height="wrap_content"
                android:text=""
                android:id="@+id/tv_longitude"
                android:layout_gravity="center_vertical"
                android:layout_marginLeft="10dp"
                android:textColor="#000000"
                android:textSize="20dp"/>
        </LinearLayout>
        <LinearLayout
            android:layout_width="match_parent"
            android:orientation="horizontal"
            android:layout_height="50dp">
            <TextView
                android:layout_width="150dp"
                android:layout_height="wrap_content"
                android:text="Address"
                android:layout_gravity="center_vertical"
                android:layout_marginLeft="10dp"
                android:textColor="#000000"
                android:textSize="20dp"/>
            <TextView
                android:layout_width="wrap_content"
                android:layout_height="wrap_content"
                android:text=""
                android:id="@+id/tv_address"
                android:layout_gravity="center_vertical"
                android:layout_marginLeft="10dp"
                android:textColor="#000000"
                android:textSize="20dp"/>
        </LinearLayout>
        <LinearLayout
            android:layout_width="match_parent"
            android:orientation="horizontal"
            android:layout_height="50dp">
            <TextView
                android:layout_width="150dp"
                android:layout_height="wrap_content"
                android:text="Area"
                android:layout_gravity="center_vertical"
                android:layout_marginLeft="10dp"
                android:textColor="#000000"
                android:textSize="20dp"/>
            <TextView
                android:layout_width="wrap_content"
                android:layout_height="wrap_content"
                android:text=""
                android:id="@+id/tv_area"
                android:layout_gravity="center_vertical"
                android:layout_marginLeft="10dp"
                android:textColor="#000000"
                android:textSize="20dp"/>
        </LinearLayout>
        <LinearLayout
            android:layout_width="match_parent"
            android:orientation="horizontal"
            android:layout_height="50dp">
            <TextView
                android:layout_width="150dp"
                android:layout_height="wrap_content"
                android:text="Locality"
                android:layout_gravity="center_vertical"
                android:layout_marginLeft="10dp"
                android:textColor="#000000"
                android:textSize="20dp"/>
            <TextView
                android:layout_width="wrap_content"
                android:layout_height="wrap_content"
                android:text=""
                android:id="@+id/tv_locality"
                android:layout_gravity="center_vertical"
                android:layout_marginLeft="10dp"
                android:textColor="#000000"
                android:textSize="20dp"/>
        </LinearLayout>
    </LinearLayout>
    <Button
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:id="@+id/btn_start"
        android:text="Get Location"
        android:layout_alignParentBottom="true"/>
</RelativeLayout>
MainActivity.java
package servicetutorial.service;
import android.*;
import android.app.Activity;
import android.app.ActivityManager;
import android.content.BroadcastReceiver;
import android.content.Context;
import android.content.Intent;
import android.content.IntentFilter;
import android.content.SharedPreferences;
import android.content.pm.PackageManager;
import android.location.Address;
import android.location.Geocoder;
import android.preference.PreferenceManager;
import android.renderscript.Double2;
import android.support.v4.app.ActivityCompat;
import android.support.v4.content.ContextCompat;
import android.support.v7.app.AppCompatActivity;
import android.os.Bundle;
import android.util.Log;
import android.view.View;
import android.widget.Button;
import android.widget.TextView;
import android.widget.Toast;
import java.io.IOException;
import java.util.List;
import java.util.Locale;
public class MainActivity extends Activity {
    Button btn_start;
    private static final int REQUEST_PERMISSIONS = 100;
    boolean boolean_permission;
    TextView tv_latitude, tv_longitude, tv_address,tv_area,tv_locality;
    SharedPreferences mPref;
    SharedPreferences.Editor medit;
    Double latitude,longitude;
    Geocoder geocoder;
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        btn_start = (Button) findViewById(R.id.btn_start);
        tv_address = (TextView) findViewById(R.id.tv_address);
        tv_latitude = (TextView) findViewById(R.id.tv_latitude);
        tv_longitude = (TextView) findViewById(R.id.tv_longitude);
        tv_area = (TextView)findViewById(R.id.tv_area);
        tv_locality = (TextView)findViewById(R.id.tv_locality);
        geocoder = new Geocoder(this, Locale.getDefault());
        mPref = PreferenceManager.getDefaultSharedPreferences(getApplicationContext());
        medit = mPref.edit();
        btn_start.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View v) {
                if (boolean_permission) {
                    if (mPref.getString("service", "").matches("")) {
                        medit.putString("service", "service").commit();
                        Intent intent = new Intent(getApplicationContext(), GoogleService.class);
                        startService(intent);
                    } else {
                        Toast.makeText(getApplicationContext(), "Service is already running", Toast.LENGTH_SHORT).show();
                    }
                } else {
                    Toast.makeText(getApplicationContext(), "Please enable the gps", Toast.LENGTH_SHORT).show();
                }
            }
        });
        fn_permission();
    }
    private void fn_permission() {
        if ((ContextCompat.checkSelfPermission(getApplicationContext(), android.Manifest.permission.ACCESS_FINE_LOCATION) != PackageManager.PERMISSION_GRANTED)) {
            if ((ActivityCompat.shouldShowRequestPermissionRationale(MainActivity.this, android.Manifest.permission.ACCESS_FINE_LOCATION))) {
            } else {
                ActivityCompat.requestPermissions(MainActivity.this, new String[]{android.Manifest.permission.ACCESS_FINE_LOCATION
                        },
                        REQUEST_PERMISSIONS);
            }
        } else {
            boolean_permission = true;
        }
    }
    @Override
    public void onRequestPermissionsResult(int requestCode, String[] permissions, int[] grantResults) {
        super.onRequestPermissionsResult(requestCode, permissions, grantResults);
        switch (requestCode) {
            case REQUEST_PERMISSIONS: {
                if (grantResults.length > 0 && grantResults[0] == PackageManager.PERMISSION_GRANTED) {
                    boolean_permission = true;
                } else {
                    Toast.makeText(getApplicationContext(), "Please allow the permission", Toast.LENGTH_LONG).show();
                }
            }
        }
    }
    private BroadcastReceiver broadcastReceiver = new BroadcastReceiver() {
        @Override
        public void onReceive(Context context, Intent intent) {
            latitude = Double.valueOf(intent.getStringExtra("latutide"));
            longitude = Double.valueOf(intent.getStringExtra("longitude"));
            List<Address> addresses = null;
            try {
                addresses = geocoder.getFromLocation(latitude, longitude, 1);
                String cityName = addresses.get(0).getAddressLine(0);
                String stateName = addresses.get(0).getAddressLine(1);
                String countryName = addresses.get(0).getAddressLine(2);
                tv_area.setText(addresses.get(0).getAdminArea());
                tv_locality.setText(stateName);
                tv_address.setText(countryName);
            } catch (IOException e1) {
                e1.printStackTrace();
            }
            tv_latitude.setText(latitude+"");
            tv_longitude.setText(longitude+"");
            tv_address.getText();
        }
    };
    @Override
    protected void onResume() {
        super.onResume();
        registerReceiver(broadcastReceiver, new IntentFilter(GoogleService.str_receiver));
    }
    @Override
    protected void onPause() {
        super.onPause();
        unregisterReceiver(broadcastReceiver);
    }
}
GoogleService.java
package servicetutorial.service;
import android.app.Service;
import android.content.Context;
import android.content.Intent;
import android.location.Location;
import android.location.LocationListener;
import android.location.LocationManager;
import android.os.Bundle;
import android.os.Handler;
import android.os.IBinder;
import android.support.annotation.Nullable;
import android.util.Log;
import java.util.Timer;
import java.util.TimerTask;
/**
 * Created by deepshikha on 24/11/16.
 */
public class GoogleService extends Service implements LocationListener{
    boolean isGPSEnable = false;
    boolean isNetworkEnable = false;
    double latitude,longitude;
    LocationManager locationManager;
    Location location;
    private Handler mHandler = new Handler();
    private Timer mTimer = null;
    long notify_interval = 1000;
    public static String str_receiver = "servicetutorial.service.receiver";
    Intent intent;
    public GoogleService() {
    }
    @Nullable
    @Override
    public IBinder onBind(Intent intent) {
        return null;
    }
    @Override
    public void onCreate() {
        super.onCreate();
        mTimer = new Timer();
        mTimer.schedule(new TimerTaskToGetLocation(),5,notify_interval);
        intent = new Intent(str_receiver);
//        fn_getlocation();
    }
    @Override
    public void onLocationChanged(Location location) {
    }
    @Override
    public void onStatusChanged(String provider, int status, Bundle extras) {
    }
    @Override
    public void onProviderEnabled(String provider) {
    }
    @Override
    public void onProviderDisabled(String provider) {
    }
    private void fn_getlocation(){
        locationManager = (LocationManager)getApplicationContext().getSystemService(LOCATION_SERVICE);
        isGPSEnable = locationManager.isProviderEnabled(LocationManager.GPS_PROVIDER);
        isNetworkEnable = locationManager.isProviderEnabled(LocationManager.NETWORK_PROVIDER);
        if (!isGPSEnable && !isNetworkEnable){
        }else {
            if (isNetworkEnable){
                location = null;
                locationManager.requestLocationUpdates(LocationManager.NETWORK_PROVIDER,1000,0,this);
                if (locationManager!=null){
                    location = locationManager.getLastKnownLocation(LocationManager.NETWORK_PROVIDER);
                    if (location!=null){
                        Log.e("latitude",location.getLatitude()+"");
                        Log.e("longitude",location.getLongitude()+"");
                        latitude = location.getLatitude();
                        longitude = location.getLongitude();
                        fn_update(location);
                    }
                }
            }
            if (isGPSEnable){
                location = null;
                locationManager.requestLocationUpdates(LocationManager.GPS_PROVIDER,1000,0,this);
                if (locationManager!=null){
                    location = locationManager.getLastKnownLocation(LocationManager.GPS_PROVIDER);
                    if (location!=null){
                        Log.e("latitude",location.getLatitude()+"");
                        Log.e("longitude",location.getLongitude()+"");
                        latitude = location.getLatitude();
                        longitude = location.getLongitude();
                        fn_update(location);
                    }
                }
            }
        }
    }
    private class TimerTaskToGetLocation extends TimerTask{
        @Override
        public void run() {
            mHandler.post(new Runnable() {
                @Override
                public void run() {
                    fn_getlocation();
                }
            });
        }
    }
    private void fn_update(Location location){
        intent.putExtra("latutide",location.getLatitude()+"");
        intent.putExtra("longitude",location.getLongitude()+"");
        sendBroadcast(intent);
    }
}
Add this dependency
compile 'com.google.android.gms:play-services:9.4.0'