The bi-articular muscle-tendon complex (MTC) in an animal's leg allows a transfer of mechanical power between adjacent joints and exertion of a large force at the toes. It is capable of storing and releasing elastic energy efficiently during motions. In our previous studies, we proposed mechanisms of the bi-articular MTC for achieving extension of the upper and lower parts of the leg and experimentally demonstrated that each mechanism allows the higher jumping motion of a legged robot. In this study, we developed a bio-inspired legged robot by integrating the upper and lower leg bi-articular MTCs and investigated the effect of their cooperative utilization on the improvement of the vertical jumping ability. A jumping motion trajectory was generated through optimization to maximize the jumping ability based on a dynamic model of the bio-inspired legged robot with these bi-articular MTCs. The simulation results of the models with and without bi-articular MTCs were compared. Finally, through jumping experiments performed by implementing the generated motion trajectory, it was confirmed that the jumping ability was improved by the cooperative utilization of those bi-articular MTCs.