It depends on why he wants to fight your ex. Has your ex done anything to you, or said anything to you, that would make your boyfriend think that your ex is trying to make a move on you, or hurt your feelings, of hurt you physically? Has your ex ever said anything offensive to your boyfriend, made a move on him, or done anything to your boyfriend, that would make your boyfriend think that your ex has shamed him? If you answer yes to any of this questions then your boyfriend is defending his honor, and he MUST fight your ex. If you answer no to any of this questions then your boyfriend is trying to impress you, which by the looks of it it seems that is not working for you, so if I were you I would tell him that you are not impress.
Sounds to me like your ex isn't your ex yet. He is still on your life somehow being thrown in your new bf's face. Get your ex out of your life, don't talk about him because it shows your still thinking about him. Then things will calm down.
If this is a serious relationship, you as a woman have a responsibility, to keep your ex out of your present relationship. Obviously he is still in the picture even if just as a friend, if your boyfriend has a problem with him. I've known guys that have gotten seriously hurt, and half of them didn't even see it coming, they were in some sort of triangle that they weren't even aware of. If you still want your ex in your life, then you will have to pick who is more important to you. Tell your boyfriend flat out that if he picks a fight with your ex it is over, and in return you will tell your ex, (in front of your guy if possible) to leave you alone, and find another girl as you are not interested. If neither one changes their attitude, then stay away from both of them as neither one cares about you, only themselves.