In order to realize that an asymmetric flow piston pump can control an asymmetric differential cylinder, a proposal about the application of an asymmetric flow-distributing axial piston pump is put forward. The new type of piston pump can output the flows with two different values to control the movement of the differential cylinder directly in the closed circuit and realize much ideal result of the control of the differential cylinder by a single pump. Also a simulation model of the hydraulic pump is established under the circumstance of SimulationX software, considering the characteristics of the movement of an individual piston, the oil compressibility, and the flow distribution area changed with the rotation angle. The key data of the pump is defined by means of digital simulation. In particular, an analysis is made on the dimension of the unloading groove of the port plate and the characteristics of the flow pulse of the pump. Furthermore, an experimental model pump is manufactured, the basic performances of the pump is tested on the experimental platform at various rotatory speeds such as pressure, flow and noise, in the end the accuracy of the principle is verified.