The objective of this paper is to design a pump that can match its delivery pressure to the aircraft load. Axial piston pumps used in airborne hydraulic systems are required to work in a constant pressure mode setting based on the highest pressure required by the aircraft load. However, the time using the highest pressure working mode is very short, which leads to a lot of overflow lose. This study is motivated by this fact. Pressure continuous regulation electrohydraulic proportional axial piston pump is realized by combining a dual-pressure piston pump with electro-hydraulic proportional technology, realizing the match between the delivery pressure of the pump and the aircraft load. The mathematical model is established and its dynamic characteristics are analyzed. The control methods such as a proportional integral derivative (PID) control method, linear quadratic regulator (LQR) based on a feedback linearization method and a backstepping sliding control method are designed for this nonlinear system. It can be seen from the result of simulation experiments that the requirements of pressure control with a pump are reached and the capacity of resisting disturbance of the system is strong.