Is there any anime series of Dragon Ball after Dragon Ball GT? I am a great fan of Dragon Ball, and I have watched almost every series and movies of Dragon Ball. However, I'm not sure if there is any other series after Dragon Ball GT.
There is no anime series of Dragon Ball after Dragon Ball GT.
Dragon Ball Kai has no independent story but is basically the story of Dragon Ball Z itself.

Instead of an anime series, the movie Dragon Ball Z: Battle of Gods was released which is in official continuity with Dragon Ball Z and therefore, before the events of Dragon Ball GT.

This year (2015) the sequel to Battle of Gods - Dragon Ball Z: Resurrection 'F' will be released.

Update

A new anime series Dragon Ball Super is going to be aired from July 2015 onwards. It's story will pick up after the events of Resurrection 'F'. 

Since the story of Dragon Ball Z has taken a significant turn by introducing the Super Saiyan God ability and other plot events, the fate of Dragon Ball GT is left hanging in the balance. At this minute, there is no official word about whether it will still exist in the continuity of the Dragon Ball Universe or not.