The behavior of a moving contact line on structured surface is analyzed by molecular dynamics. The analyses were made by using a Couette flow geometry where two immiscible fluids are sheared between two parallel plates, one of which is characterized by step-structured surface with a depth of one or more times of the wall lattice constant a_0, set to be almost equal to the average distance between liquid atoms. The contact lines strongly tend to be captured at the edge of the steps and the minimum contact angle is dependent on the depth of the steps. When the depth is identical to as the contact angle decreases by several tens degrees from that for the plane surface before the contact line leaves the edge of the steps. When the depth is twice a_0, the contact lines stay at the step edge until the contact angle decreases almost zero.