I hate to tell you this but all you can do is be very open and honest about everything. Do your best not to give her anything to feel jealous about...
Beyond that...
Jealousy is HER feeling, her emotion. You cannot control another person's feelings or actions. It's a feeling of fear and control. We feel jealous when we're afraid that our partner will leave us or we feel jealous when our partner does not do what we tell them to do (control) or when they feel threatened by a perceived rival.
Most likely her feelings of jealousy have nothing to do with you, but come from something in her history - feelings of abandonment from childhood, being burned by another lover, watching her mother have a bad relationship, etc...
You can't convince her - it's something that she has to realize herself.
The best thing that you can do is to try to get her to talk about the things that make her feel jealous. Just listen, don't argue with her feelings. Don't try to fix it, just listen and accept what she's telling you. Recognize that these feelings are not your fault and that you have no control over them. They are just her feelings, nothing more, nothing less...