how to make a animated splash screen like below image in iOS 9.3.

Basically, you can't make an animated splash screen. However, you can duplicate the launch screen in your storyboard and make it the entrance-view controller (VC) of your app. Then when the view is loaded, you can start your animation. As a final result, you will have an "animated splash screen."
The sequence progresses like this:
App starts → display static launch screen → transition to entrance-VC, which won't be visible to the user because the scenes look the same → entrance-VC view is loaded as an animation.
In summary, treat your launch screen's .xib file as the first frame of your animated launch screen.