The gear pump-motor unity machine, which was composed of the planetary gear pump and multiple gear variable-displacement motor was designed by the author. In this paper, based on the physical model, mathematical models of the machine were established. The transfer functions were deduced and the block diagrams of the transfer functions were drawn. The dynamic characteristics of the machine were analyzed. While the damping coefficient is rising, the oscillation amplitude will decrease. While the damping coefficient is bigger, both overshoot fluctuation are smaller. While the steady-state adjusting time is decreasing, dynamic response characteristics of the motor significantly improved. While the leakage coefficient is rising, the response speed of motor will improve, but the excessive leakage coefficient increases will lead to larger leakage, which seriously impact the motor performance. The dynamic characteristics of the machine were analyzed. As of ωn>0 and ξ>0, gear-pump motor unity machine is inevitably stable.