To improve the reliability and performance of hydraulic axial piston pump, the reliability design method of volumetric efficiency, one of the main performance indexes of axial piston pump, was investigated. The instantaneous leakage flow rate and volumetric efficiency of the axial piston pump with the cylinder body at any instantaneous angle are deduced by comprehensively analyzing the instantaneous leakage of a single piston. The reliability and reliability sensitivity analysis method of the axial piston pump are established by using the random perturbation theory and the fourth-order moment technology, and the accuracy and rationality of the proposed method are verified by Monte Carlo method. The results show that the reliability of the hydraulic axial piston pump fluctuates periodically with the angle of the cylinder block, the reliability is the lowest when the piston passes through the top dead center, although the reliability fluctuates relatively greatly when the number of pistons is 9, but its overall reliability level is higher than that of the 8 pistons. The clearance between the slipper and the swash plate, and between the cylinder block and the port plate has a greater impact on the reliability, while the clearance between the piston and the piston chamber, and between the slipper and the piston ball hinge has a smaller impact. The method presented in this paper provides a theoretical reference for the research, design, process and quality control of axial piston pump.