Time optimal control method for quadruped walking robots has been developed and installed into a practical robot system. The fastest trot walk and the trajectory of swing legs have already been obtained by our previous study. In this study, we designed velocity trajectories of the body and swing legs. Then, the design method of velocity trajectory that can accelerate to maximum speed in the shortest time and can decelerate to stop in the shortest time is established by combining velocity trajectory of the acceleration part and deceleration part of the body. Finally, we verified the simulation results.