In this paper, a new leg mechanism that mimics the function of the musculoskeletal structures of the thigh of the mammals is proposed. The bi-articular muscle-tendon complex of the thigh makes it possible to drive the hip and the knee joints as well as store and release the elastic energy, and it contributes to extension of the leg at the jumping and swinging of the leg during running. A mechanism with the function is introduced to a bipedal robot that mimics the hind limbs of mammals. In order to verify the effect of the mechanism, motion planning for the vertical jumping is performed for the models with and without the mechanism by a nonlinear optimization simulation. The motion trajectory is optimized to maximize the jumping height and the derived results show that the jumping height can be improved by the mechanism. Through the experiments, it is confirmed that the jumping height by the bipedal robot with the proposed mechanism was improved and the effectiveness of the proposed mechanism is shown.