Mirror map is a central object in the study of mirror symmetry. They are obtained in hypergeometric series by solving Picard-Fuchs equations. In this talk, I will explain a geometric meaning of mirror maps for toric varieties in terms of counting of holomorphic discs bounded by Lagrangian submanifolds. It is motivated by the study of SYZ mirror symmetry. This is a joint work with K. Chan, N.-C. Leung and H.-H. Tseng.