How do I persuade my girlfriend's mother to marry

Dear Shivkumar, welcome to eTI.

You asked question in very vague manner, it looks as if you are asking how to make Mother of girlfriend to get married to you. However, jokes apart, we all know you want to convince mother of your girlfriend so that you and your girlfriend can marry each other.

But, to suggest you anything, you need to provide more details, lot more details than simply asking one line question.