I wouldn't say that there is anything wrong with you. Most people experience jealousy at one point or another during their relationships. The key is to understand why you are feeling the way you are and then to take steps to fix it. Otherwise, you may find that your jealousy winds up driving your girlfriend away.
Here are a couple of the most common reasons why people feel jealous: 
- Insecurity or low self-esteem. If this is what is causing your jealousy, you may feel like you are not good enough or that you don't have enough to offer to keep someone interested in you. This can cause you to have critical thoughts toward yourself. For instance, when your girlfriend mentions a past boyfriend, you may subconsciously worry that you aren't as attractive or funny as them, which can cause you to feel pangs of jealousy. Even worse, it may even cause you to feel disappointed with yourself for not being good enough, which can further damage your self-esteem.
- Obsessive thinking. You may find that your brain is always on, worrying about one thing or another. This type of obsessive thinking can lead you to overanalyze every small move that your partner makes, reading things into their actions that really aren't there. It can also cause you to come up with scenarios or situations that don't actually exist. For instance, if your girlfriend doesn't immediately text you back, you may worry that she is with someone else or that she doesn't love you anymore when in reality she is just in the shower or doing something else and is away from her phone.
The problem with jealousy is that in a way it becomes a self-fulfilling prophecy. When you overreact to something your partner does or worry about whether or not they love you all the time, it can create distance in your relationship. Even if you don't actually say anything to your girlfriend about how you are feeling, chances are she will be able to pick up on it. She may feel like she is always being judged or like she has always done something wrong just from the subtle queues that you inadvertently give off when you are feeling jealous. This could eventually wind up driving her away.
If you want to prevent that, you need to find a way to control your jealous feelings. A good place to start is by working on building your self-esteem. Until you realize that you have just as much to offer as anyone else she has been with (or could be with) you will always feel those negative, jealous feelings. Try to become aware of your negative, critical inner voice that makes you feel inferior or that makes you doubt yourself. 
For instance, when you see your girlfriend laughing with her friends, your inner voice may tell you that you aren't funny and that you can't make her laugh like that. Counteract that voice with a more positive, realistic thought. You might remind yourself of a time when she did laugh at one of your jokes, or think of other positive aspects of your relationship that you can give her that her friends can't.
If you start having obsessive thoughts about her past boyfriends or about whether or not she really loves you, remind yourself that you can't change the past or the future. Instead, you have to focus on the here and now. Right now your girlfriend loves you and is with you...not with one of her ex-boyfriends. She has chosen you, which means that she must see something valuable in you. If she wanted to be with someone else, she would be. Always try to bring yourself back to the present moment rather than worrying about things that happened in the past or that may happen in the future.
Changing your internal dialogue can be extremely challenging. However, each time you correct one of your jealous thoughts, you will break down a little more of the wall that is keeping you from fully enjoying your current relationship. Before you know it, those jealous feelings will be minor blips on your radar rather than overwhelming thoughts.
P.S. This video has some more great tips on overcoming jealousy: