It is possible to customize searchview by using appcompat v7 library.I used appcompat v7 library and defined custom style for it.
In drawable folder put bottom_border.xml file which looks like this:
 <?xml version="1.0" encoding="utf-8"?>
 <layer-list xmlns:android="http://schemas.android.com/apk/res/android" >
 <item>
  <shape >
      <solid android:color="@color/blue_color" />
  </shape>
 </item>
 <item android:bottom="0.8dp"
   android:left="0.8dp"
   android:right="0.8dp">
  <shape >
      <solid android:color="@color/background_color" />
  </shape>
 </item>
 <!-- draw another block to cut-off the left and right bars -->
 <item android:bottom="2.0dp">
  <shape >
      <solid android:color="@color/main_accent" />
  </shape>
  </item>
 </layer-list>
In values folder styles_myactionbartheme.xml: 
 <?xml version="1.0" encoding="utf-8"?>
 <resources>
  <style name="AppnewTheme" parent="Theme.AppCompat.Light">
    <item name="android:windowBackground">@color/background</item>
    <item name="android:actionBarStyle">@style/ActionBar</item>
    <item name="android:actionBarWidgetTheme">@style/ActionBarWidget</item>
  </style> 
  <!-- Actionbar Theme -->
  <style name="ActionBar" parent="Widget.AppCompat.Light.ActionBar.Solid.Inverse">
    <item name="android:background">@color/main_accent</item>
    <!-- <item name="android:icon">@drawable/abc_ic_ab_back_holo_light</item> -->
  </style> 
  <style name="ActionBarWidget" parent="Theme.AppCompat.Light">
    <!-- SearchView customization-->
     <!-- Changing the small search icon when the view is expanded -->
    <!-- <item name="searchViewSearchIcon">@drawable/ic_action_search</item> -->
     <!-- Changing the cross icon to erase typed text -->
   <!--   <item name="searchViewCloseIcon">@drawable/ic_action_remove</item> -->
     <!-- Styling the background of the text field, i.e. blue bracket -->
    <item name="searchViewTextField">@drawable/bottom_border</item>
     <!-- Styling the text view that displays the typed text query -->
    <item name="searchViewAutoCompleteTextView">@style/AutoCompleteTextView</item>        
  </style>
    <style name="AutoCompleteTextView" parent="Widget.AppCompat.Light.AutoCompleteTextView">
     <item name="android:textColor">@color/text_color</item>
   <!--   <item name="android:textCursorDrawable">@null</item> -->
    <!-- <item name="android:textColorHighlight">@color/search_view_selected_text</item> -->
  </style>
 </resources>
I defined custommenu.xml  file for displaying menu:
 <menu xmlns:android="http://schemas.android.com/apk/res/android"
   xmlns:com.example.actionbartheme="http://schemas.android.com/apk/res-auto" >  
  <item android:id="@+id/search"
      android:title="@string/search_title"
      android:icon="@drawable/search_buttonn"
      com.example.actionbartheme:showAsAction="ifRoom|collapseActionView"
        com.example.actionbartheme:actionViewClass="android.support.v7.widget.SearchView"/>        
  </menu>
Your activity should extend ActionBarActivity instead of Activity.
 Here is onCreateOptionsMenu method.
  @Override
  public boolean onCreateOptionsMenu(Menu menu) 
  {
    // Inflate the menu; this adds items to the action bar if it is present.
    MenuInflater inflater = getMenuInflater();
    inflater.inflate(R.menu.custommenu, menu);
  }
In manifest file:
  <application
      android:allowBackup="true"
      android:icon="@drawable/ic_launcher"
      android:label="@string/app_name"
      android:theme="@style/AppnewTheme" >
For more information see this url:
Here http://www.jayway.com/2014/06/02/android-theming-the-actionbar/