— This paper discusses jumping pattern generation for a serial link robot in order to maximize its jump height under torque limitation. By applying a genetic algorithm (GA) for determining torque assignment, we obtain various jumping patterns with respect to the torque limitation for a fixed mass of the robot. With the increase of the torque limitation, doubleleg based jump, single-leg based jump, and spring-type jump are generated for achieving the largest jump height. Under an additional joint angle limitation, we also obtain an interesting solution where one end of the link is first lifted up and the other end finally kicks the ground strongly.