I don't think you can do anything to convince her that your parents welcome her if, in fact, they don't. You can tell her that it doesn't matter to you what they think of her, that they'll come around when they see how wonderful she is, etc. etc. But if they don't change their tune, this is something that you're both going to have to live with. And if she can't live with it, I'm afraid there's not much you can do.
That said, you can talk to your parents about changing their behavior. You can't make them like your girlfriend, although you can explain why you like her so much. What are they doing that your girlfriend perceives as "not welcoming"? Are they being rude to her? Saying things in front of her? You can tell your parents that that must stop or you just won't spend any time around them. (Depending on how old you are, that may or may not work - if you're an adult living on your own, you can do whatever you want, but it'd be hard to avoid them if you're still living with them). Hopefully they'll see how much it means to you and at least make an effort to be civil.
Good luck!
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"If ten million people believe a foolish thing, it is still a foolish thing."
- Anatole France
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