Have you left something like a bag on the passenger seat? This would trigger off the seatbelt alarm.
If not then the seat belt end may not be operating the switch in the seat belt stalk when it is done up. The stalk could be damaged or dirty. May need a new stalk if the old one can't be cleaned up or repaired. Try a scrap yard for a replacement stalk if you have to replace it.
ChicksFan, December 2013