Grasping a non-cooperative ''customer satellite'' with a robotic arm is a challenging task for on-orbit services of spacecraft since the collision between the robot and the target is inevitable and the dynamic behaviors of the two objects are hard to control after the collision. To grasp successfully, the contact between the space robot and the target is hoped to be maintained after the collision. In this paper, the contact control problem for grasping a non-cooperative satellite is studied. First, to simulate the contact conditions as realistic as possible, the multibody dynamics, the modified Hertz contact, and the contact detection theory are employed to establish a grasping dynamics model. Then, based on the study on the dynamic behavior of the two-ball collision problem, a hybrid control scheme with damping and attitude tracking controllers is proposed. By this scheme, the control goal, i.e. maintaining the contact between the robot and the target, can be realized after multiple collisions. Finally, numerical simulations are performed to validate the proposed control scheme, and the results demonstrate its effectiveness in grasping a non-cooperative tumbling satellite.