Is it normal to be in a relationship with low self esteem girls?

thats a very vague question. You have not said how long you been together, what your relationship is like with her, how she makes you feel, and because of that there is little feedback most of us can give you. Do you know what causes her low self esteem? if not then why dont you try and change that. Tell her she is beautiful, take her shopping ( i dont mean spend a lot of money) buy her something small she likes. Do little things that make her think you like/love her, communicate more to improve your connection with her.

yeah dude if you help her realize how beautiful she is to you it will be worth it

Agree with chatter289, little things mean big things to us and telling her how good she looks and how good she makes you feel will hopefully give her more self confidence so you both win

Hard to say. Being in a relationship could help her or it might not.

I dont know do you enjoy being in the relationship?

You would constantly have to reassure her all the time if her self esteem is that low, is that something you want to do?

In my humble cynical opinion, it's wrong to believe that anyone would change for you. If you don't like the fact that she struggles with her self image and is unsure of herself a lot of the time, look elsewhere for love.