Your kitty should be past teething problems, unless as Februa mentioned he's got teeth he didn't shed despite having his adult teeth in.
The most important thing is to not let him be bitey with you. If he nips at you, immediately stop whatever you're doing with him. Give him a short sharp puff of air in the face and walk away. He'll catch on quickly that biting is not a way to get your attention, and the puff of air in his face will startle him but not scare or anger him.
You may want to consider dropping lots of bendy straws around. This helped all our kitties get through the "bitey" stage. They're apparently lots of fun to chew on, but they're a kind of plastic they can't chew through before you see the straw is starting to come apart, so it's no danger to them.