The axial piston pump (APP) is the core power component of hydraulic systems. Its friction-pair wear can cause the degradation of piston pump performance until the function is completely lost or the service life is terminated. The slipper pair, prone to wear failure, is selected as the research object. The prediction method for the eccentric wear of the slipper pair is established, and the gradual change rules of the performance with wear accumulation are explored. Based on the elastohydrodynamic lubrication model of the slipper pair, the micro-surface rough peak contact and the stress state of the slipper pair are analyzed, and the mixed lubrication model of the slipper pair is established. Based on two-body abrasive wear and Archard adhesive wear models, grid discretization of a sealing belt of the slipper pair is carried out to improve the prediction method for eccentric wear of the slipper pair. The effectiveness of the proposed method is verified by a surface morphology analysis of the worn slipper. The results showed that the wear depth and wear width of the outer edge of the slipper bottom surface are positively correlated with the oil discharge pressure and the inclination angle of the swashplate, and negatively correlated with the rotational speed and the dynamic oil viscosity. The outer edge of the slipper is wedged after eccentric wear, and the hydrodynamic effect of the lubricating oil film of the slipper pair is enhanced. Hence, proper wear can improve the lubrication performance of the slipper pair.