We do not know anything about Mary’s genealogy from Sacred Scripture. In fact, the Bible doesn’t even give us her parents’ names. Tradition, however, gives their names as Sts. Joachim and Anne. They are written about in a book that did not get collected into the canon of Scripture called the Protoevangelium of St. James — sort of a prequel to the Gospels, which focuses on the early life of Mary. There we learn that Joachim and Anne are holy and God-fearing people. They prayed for a child after a long period of barrenness, and Mary was conceived by them.
Michael R. Heinlein is editor of Simply Catholic. Follow him on Twitter @HeinleinMichael.