In Islam, Imran is the father of Mary and the grandfather of Jesus. However, due to extenuating circumstances, Mary was raised primarily by her uncle Zakariya.

It says in the Qur'ān, Sūrat Ãl-Imrān (lit. "The chapter of the family of Imrān", note that as with most other Sūrats of the Qur'ān this name does not mean that it is dedicated entirely to the family of Imrān):

35. (Remember) when the wife of Imrān said: "O my Rabb (Lord)! I have vowed to You what (the child that) is in my womb to be dedicated for Your services (free from all worldly work; to serve Your place of worship), so accept this from me. Verily, You are the All-Hearer, the All-Knowing."

36. Then when she gave birth to her child, she said: "O my Rabb! I have given birth to a female child," - and Allah knew better what she brought forth - "And the male is not like the female, and I have named her Maryam (Mary), and I seek refuge with You for her and for her offspring from Shaitan (Satan), the outcast."

37. So her Rabb accepted her with goodly acceptance. He made her grow in a good manner and put her under the care of Zakariyya (Zacharia). Every time he entered Al-Mihrāb (her private room) to visit her, he found her supplied with sustenance. He said: "O Maryam! From where have you got this?" She said, "This is from Allāh." Verily, Allāh provides sustenance to whom He wills, without limit.

Had she bore a son she would have named him "Abdullah" (the servant of Allah), but she bore a daughter, so she named her "Maryam" (the maidservant of Allah).

(Interpretations and meanings of the Noble Qur'ān in the English language. Dar-us-Salaam publications).