Well I have implemented by CustomWebView and GestureDetector:
CustomWebView.java:
public class CustomWebView extends WebView {
    private GestureDetector gestureDetector;
    public CustomWebView(Context context) {
        super(context);
    }
    public CustomWebView(Context context, AttributeSet attrs) {
        super(context, attrs);
    }
    public CustomWebView(Context context, AttributeSet attrs, int defStyle) {
        super(context, attrs, defStyle);
    }
    @Override
    protected void onScrollChanged(int l, int t, int oldl, int oldt) {
        super.onScrollChanged(l, t, oldl, oldt);
    }
    @Override
    public boolean onTouchEvent(MotionEvent ev) {
        return gestureDetector.onTouchEvent(ev) || super.onTouchEvent(ev);
    }
    public void setGestureDetector(GestureDetector gestureDetector) {
        this.gestureDetector = gestureDetector;
    }
}
web_fragment.xml:
<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:background="@android:color/transparent"
    android:orientation="vertical">
   <com.customview.CustomWebView
            android:id="@+id/customWebView"
            android:layout_width="match_parent"
            android:layout_height="match_parent"
            android:focusable="true" />
</LinearLayout>
CustomeGestureDetector clss for Gesture Detection (I have added in Fragment):
private class CustomeGestureDetector extends GestureDetector.SimpleOnGestureListener {
        @Override
        public boolean onFling(MotionEvent e1, MotionEvent e2, float velocityX, float velocityY) {
            if(e1 == null || e2 == null) return false;
            if(e1.getPointerCount() > 1 || e2.getPointerCount() > 1) return false;
            else {
                try {
                    if(e1.getY() - e2.getY() > 20 ) {
                            // Hide Actionbar
                        getSupportActionBar().hide();
                        customWebView.invalidate();
                       return false;
                    }
                    else if (e2.getY() - e1.getY() > 20 ) {
                            // Show Actionbar
                        getSupportActionBar().show();
                        customWebView.invalidate();
                       return false;
                    }
                } catch (Exception e) {
                    customWebView.invalidate();
                }
                return false;
            }
        }
    }
WebFragment.java:
private CustomWebView customWebView;
customWebView= (CustomWebView) view.findViewById(R.id.customWebView);
customWebView.setGestureDetector(new GestureDetector(new CustomeGestureDetector()));
It works fine for me, hope it would help you.