Degradation state recognition and failure prediction are the key steps of prognostic and health management (PHM), which directly affect the reliability of the equipment and the selection of preventive maintenance strategy. Given the problem that the distinction between feature vectors is not obvious and the accuracy of fault prediction is low, a method based on multi-class Gaussian process classification and Gaussian process regression (GPR) is studied by the vibration signal and flow signal in six degraded states of the axial piston pump. For degradation state recognition, the variational mode decomposition (VMD) was used to decompose the vibration signal, and obtaining intrinsic mode function (IMF) components with rich information. Subsequently, multi-scale permutation entropy (MPE) was employed to select feature vectors of IMF components in different states. In order to reduce feature dimensions and improve recognition performance, ReliefF was used to select feature vectors with high weight, then a method based on multi-class Gaussian process classification was established by using these feature vectors to realize the research on the degradation state recognition. The test results demonstrate that the method can effectively identify the degradation state. Its recognition rate reaches 98.9%. Besides, for failure prediction, through the analysis of the wear process and wear mechanism of the valve plate, the curve fitting between the flow and the wear amount was performed by GPR to realize the failure prediction of the axial piston pump. Depending on the evaluation index, the GPR obtained a better failure prediction effect. The results will assist in the realization of predictive maintenance, and which also has significant practical value in project items.