If I understand the kind of thing you describe - a small nip with the front teeth, often several in quick sucession? - it is a sign of affection.
If you were another dog with a nice covering of hair it would be felt as a very gentle tug, not at all painful.
As you have found out it can hurt human skin quite a lot!

Spend some play time with this dog alone. As soon as a nip occurs say, "Ow!", drop whatever you are doing, turn your back on the dog and cross your arms. Look upwards while you do this. Don't go back to the game until the dog has calmed down and has wandered away from you a little (this may take some time at first!). Call him back, ask for a sit and then give quiet praise before resuming the game.
This is not a serious problem really - the dog justs needs his bite inhibition heightened to include "love bites" to humans.