I am looking for Like Button to be shown in my ios native app, users of that app have already connected to app via facebook account.
there are several questions rela
This still can't be done directly using the graph api ( to the best of my knowledge ). What you can do is open a webview to the page you want the user to like. If you're rewarding their liking your app or something, when they close the webview (you'll have to provide a close button), you can use the graph api to check whether they like your app page. As far as I can tell this is the best current solution - and seems to be the approach taken by mobile games.
That said, I haven't used Facebook SDK 3 yet, so there may be something in there that could help you.