Q. 1. Who were the parents of the Blessed Virgin Mary?
A. 1. The parents of Mary, the maternal grandparents of Jesus were Saint Anne and Saint Joachim.
Quoting from " The Catholic Encyclopedia. Vol. 15. New York: Robert Appleton Company, 1912. 6 Feb. 2010.
"Though few commentators adhere to this view of St. Luke's genealogy, the name of Mary's father, Heli, agrees with the name given to Our Lady's father in a tradition founded upon the report of the Protoevangelium of James, an apocryphal Gospel which dates from the end of the second century. According to this document the parents of Mary are Joachim and Anna. Now, the name Joachim is only a variation of Heli or Eliachim, substituting one Divine name (Yahweh) for the other (Eli, Elohim). The tradition as to the parents of Mary, found in the Gospel of James, is reproduced by St. John Damascene , St. Gregory of Nyssa , St. Germanus of Constantinople , pseudo-Epiphanius , pseudo-Hilarius , and St. Fulbert of Chartres . Some of these writers add that the birth of Mary was obtained by the fervent prayers of Joachim and Anna in their advanced age. As Joachim belonged to the royal family of David, so Anna is supposed to have been a descendant of the priestly family of Aaron; thus Christ the Eternal King and Priest sprang from both a royal and priestly family ."
 hom. I. de nativ. B.V., 2, P.G., XCVI, 664
 P.G., XLVII, 1137
 de praesent., 2, P.G., XCVIII, 313
 de laud. Deipar., P.G., XLIII, 488
 P.L., XCVI, 278
 in Nativit. Deipar., P.L., CLI, 324
 cf. Aug., Consens. Evang., l. II, c. 2