Custody is a kind of guardianship and dominance over the maintenance and education of children and the insane. When the child's parents are separated, the issue of custody and the priority of each of them for care and custody of the child are proposed. Opinions of scholars about the qualification of parents in childhood are different. Renowned scholars hold that the mother is more qualified for the custody of a child up to the age of 2 and if the child is a girl up to the age of 7.Although civil law follows the famous idea of the past, by changing this idea now the custody of a child, whether a boy or a girl up to the age of 7 is with mother. According to the Convention of Eliminaling Discrimination against Women, which was passed in 1979 in order to protect women’s rights, any act, practice procedure, culture, and common tradition that may impair the equality of men and women in all fields- political, economical, social, and cultural- is considered discrimination. It seems that Article 2 of Act 5 of the Convention has no discrepancy with our law concerning child custody in that it propounds the equal responsibility of men and women in upbringing children. In the present paper, by examining the custody rights in Iran’s law and Islamic law, and comparing it with the Convention of Eliminating Discrimination against women, we come to the conclusion that according to the law of custody in Iran, in the case of separation of parents, the mother will take the custody of the child up to the age of 7, which is considered discrimination with regard to Article 2 of Act 5 of the Convention of Eliminating Discrimination against women.