Or at least, appearance wise.
In his first appearances we can guess he's between the human equivalent of 14 - 18.
However in his next, which takes place months afterwords, he doesn't seemed to have aged at all to me. Maybe I haven't just seen the movie in a while, but he didn't seem to change at all in any way except maybe more loyal to his mom and less jealous of Kovu/more mature.
He could have already been adult sized/ended "puberty" in his first appearance however almost everyone else changed somehow. Be it physically or mentally.