Add icon near hamburger to navigation drawer

Question

Actually I have this hamburger icon in my navigation drawer auto generated by eclipse:

I would get this result:

Answer 1

First thing, always show what you have tried resolve your query.
Second to answer this, try

ActionBar actionBar = getSupportActionBar();
actionBar.setLogo(R.drawable.ic_launcher);
actionBar.setDisplayUseLogoEnabled(true);
actionBar.setDisplayShowHomeEnabled(true);

Answer 2

将此放在您的小部件中

android:drawableRight="@drawable/image"