public native void enableDragging() /*-{
var marker = this.@com.gwtext.client.core.JsObject::getJsObj()();
marker.setDraggable(true);
}-*/;

It solved the problem. Now, the marker is draggable. Now the next issue is that I want to track the dragging marker. So I would need a listener so added the following function to MyGoogleMarker.

public native void addEventListener(String event, MyEventHandler listener) /*-{
var marker = this.@com.gwtext.client.widgets.map.Marker::toGoogle()();
marker.addListener(event, function(llp) {
listener.@com.findmeacab.project.client.MyEventHandler::execute(Lcom/google/gwt/core/client/JavaScriptObject;)(llp);
});
}-*/;

Where MyEventHandler is the following interface.
package com.findmeacab.project.client;
import com.google.gwt.core.client.JavaScriptObject;
public interface MyEventHandler {
public void execute(JavaScriptObject arg);
}
I do not know where I am making mistake the event never triggers when I make the call.

MyEventHandler myEventHandler = new MyEventHandler() {
@Override
public void execute(JavaScriptObject arg) {
System.out.println(“Drag End”);
}
};
marker.addMyEventListener(“dragend”, myEventHandler);

Any suggestion will be highly appreciated

-Ali