What do I have to do to make my girlfriend trust me?

My girlfriend and I have been together for four months now. I love her with all my heart but she is always jealous of other girls and thinks that I am going to cheat on her. Tonight she got mad at me for telling a girl thank you for wishing me a Merry Christmas, she got very angry and said ” I really don’t wanna be around you that much” that hurt me so much because it is Christmas day she should be happy that she is spending this wonderful day with me. I try so hard to show her that I wont cheat on her and I even made her a promise that I would never cheat on her and still it seems she don’t trust me.