Sore Losers

I'm making this post to ask for advice. I'm a member of an amateur clan. I get along with everyone in the clan, and we generally all have a good time. My problem focuses on a certain, unnamed member of my clan. I'm really good friends with him, but whenever I beat him, he gets really mad and it hurts our friendship. I'm a league above him, so I usually win. I could simply refuse to play him, but he gets annoyed when I suggest this. I really like him as a friend, but I'm not sure how to resolve this issue :(