Anne was the daughter of Ralph Lowe but her mother is unknown. The date and place of her birth have not been found.
Her husband was Oswald Moseley. They were married, but the date and place have not been found. Their eight known children were Nicholas (?-?), Oswald (?-1653), Samuel (?-?), Francis (?-?), Mary (?-?), Margaret (?-?), Anne (?-?) and Edward (c1616-1695).