How do you convince your parents into letting you be a model?

Ultimately, it is up to your parents to decide whether or not to let you model, especially if you are underage. It is helpful to do research about the modeling industry, what it takes to get signed, if you meet the requirements and understand the nature of the work. The more you know about modeling, it will show your parents how important it is to you and that you are serious about pursuing it. If they still don't agree, then there won't be much you can do about it unless they end up changing their minds or you turn 18 and can make that decision for yourself.