For quadruped robots with springy legs, a successful jump usually requires both suitable elastic parts and well-designed control algorithms. However, these two problems are mutually restricted and hard to solve at the same time. In this study, we attempt to solve the problem of controller design with the help of a robot without any elastic mounted parts, in which the untethered robot is made to jump on a trampoline. The differences between jumping on hard surfaces with springy legs and jumping on springy surfaces with rigid legs are briefly discussed. An intuitive control law is proposed to balance foot contact forces; in this manner, excessive pitch oscillation during hopping or bounding can be avoided. Hopping height is controlled by tuning the time delay of the leg stretch. Together with other motion generators based on kinematic law, the robot can perform translational and rotational movements while hopping or bounding on the trampoline. Experiments are conducted to validate the effectiveness of the proposed control framework.