Abstract: A hopping cycle of the pneumatically actuated one-legged robot includes stance phase and flight phase. By virtue of dynamics, thermodynamics, hydrodynamic, collision theory and control theory, a comprehensive mathematical model of a hopping cycle of the pneumatically actuated one-legged robot is proposed, which includes the landing collision between the foot and the ground, the buffering stage and acceleration stage in stance phase, the shock of take-off by the leg at the moment of take-off, and the process of piston positioning in flight phase. A combined simulation model of a hopping cycle of the robot is built in Matlab. Simulation study is made on the effect law of main influential factors on the landing collision, the shock of take-off and the hopping height of the one-legged robot. And the regularity understanding on the effect law is achieved. The main influential factors include: preset values of the chambers pressure of the lower chamber and the piston position at the landing moment, relative coordinate of conversion between charge and exhaust. Value ranges and the better values of the above factors which can realize higher jump, lower jump and equal height jump of the robot are obtained. A test rig of vertical hopping of the one-legged robot is built, and effect laws of the main influential factors on the hopping process of the robot are investigated. The simulation results are in good agreement with the experiments results.