what can i do to improve their relationship?

You don't say the ages, but if your brother is a kid, he's probably jealous of the time you're spending outside the family and he's worried about "losing" you to your new love.

Reassure your brother that, even though you have a new relationship, you still love him and the family and that will never change. Don't neglect your brother; spend some time with him.

Can you bring your new boyfriend over and have him spend some time with the family, too; something like having dinner together, playing games, or just watching TV.

Probably when your brother gets to know your boyfriend, he will learn to like him. And if you don't have any other brothers in the family, your brother might enjoy having an older guy around as a role model/sounding board/etc.

my best friend did the same thing when i started dating my boyfriend. I don;t think there is much you can do. It just doesn't make sense and you can't tell a crazy person they're crazy. Well you can but they don't get it. I think it'll work itself out in time when he sees that you are happy and that your boyfriend isn't going anywhere.

Just be yourself. It doesn't matter if it's good enough for someone else.