By analyzed the working principle and function of constant pressure variable piston pump, the hydraulic mechanical signal library was used in AMESim to establish the simulation model of constant pressure variable piston pump. By setting all parameters of the simulation model according to the actual structure and size of constant pressure variable piston pump, the simulation research of the constant pressure variable piston pump of static and dynamic characteristics was carried out. The constant pressure variable piston pump of working pump inlet pressure and flow characteristic curve was concluded. Comparing it with the constant pressure variable piston pump of flow characteristic curve of pressure sample, there was a certain alignment. It is shown that the type of the constant pressure variable piston pump of simulation model is relatively accurate. At the same time, the constant pressure variable piston pump of rise time and overshoot volume are concluded.