How to get current selected tab index in TabLayout?

Use OnTabSelectedListener.

And then in this listener get the getPosition().

Something like this:

tabLayout.setOnTabSelectedListener(new TabLayout.OnTabSelectedListener(){
    @Override
    public void onTabSelected(TabLayout.Tab tab){
        int position = tab.getPosition();
    }
});

UPDATE

This method setOnTabSelectedListener() is deprecated . Use addOnTabSelectedListener(OnTabSelectedListener)

setOnTabSelectedListener is now deprecated. you can use addOnTabSelectedListener instead. To remove the listener you can use removeOnTabSelectedListener

 mTabLayout.addOnTabSelectedListener(new TabLayout.OnTabSelectedListener() {
        @Override
        public void onTabSelected(TabLayout.Tab tab) {
            int position = tab.getPosition();
        }

        @Override
        public void onTabUnselected(TabLayout.Tab tab) {
        }

        @Override
        public void onTabReselected(TabLayout.Tab tab) {
        }
    });