How to deal with jealousy?

How do you deal with a really jealous bf (or significant other)? My bf is really jealous, though he swears he's not. He gets nervous every time i'm on my phone texting someone or my phone rings, he always asks who it is. I feel like he's very insecure with himself. But how do you deal with the whole issue 'if you have nothing to hide, why can't u show me?' It really wears a relationship thin and kind of turns me off. I mean, afterall, what's a relationship without trust?