Technically it depends on whether it is the maternal grandmother, if she was Jewish then you'd be as Jewish as anyone. Different Jewish movements would have different views on this, Liberals believe that being culturally Jewish is more important than being born Jewish and would probably recommend to someone who had never had any kind of Jewish upbringing to go through some kind of Jewish education, or even a conversion if they wanted to be considered Jewish. To the Orthodox, it's halachah (Jewish law) alone that matters.