Boyfriend wrongly accuses me of cheating.

Aimee
So my boyfriend of 6 months (give or take) has just started accusing me of cheating. He makes comments almost every day now. Things like "is that your lover texting" or shit like that. He's read my messages and Facebook and even went through my computers history. 
I have never cheated, I wouldn't cheat I think it's low and disgusting behaviour. I think I put a lot of effort into this relationship but it doesn't matter cause he's resilient with these cheating jokes/comments.
It's really frustrating cause no matter what I say he doesn't believe me. I don't know what to do.