Where in the tank does he swim? Is he chasing his reflection in the glass, or is he just swimming in circles in the middle? Is he chasing his tail, potentially? Long finned bettas will sometimes bite off their fins if they're bored.
What size is the tank? What else is in there (decor, plants, etc)? There are a couple reasons he's doing this - he's chasing his reflection, which is normal but if it's dark that's probably not it (if you leave his tank light on at night though, it could be this), or he's bored.