It'll have to be something he has to work with himself, I think. I have anxiety problems as well (that I'm trying to overcome), and while it's gotten better for me, I don't do well with a few people I don't know. If it's just 1 person I don't know, I usually can get along fine. Even with groups of friends i'm fine.
I don't think there is too much you can do for your friend, besides offering help, and not pushing him into the spotlight