Axial piston pumps are crucial for the safe operation of hydraulic systems and usually work under variable operating conditions. However, deterioration status recognition for such pumps under variable conditions has rarely been reported until now. Therefore, it is valuable to develop effective methods suitable for processing variable conditions. Firstly, considering that information entropy has strong robustness to variable conditions and empirical mode decomposition (EMD) has the advantages of processing nonlinear and nonstationary signals, a new degradation feature parameter, named local instantaneous energy moment entropy, which combines information entropy theory and EMD, is proposed in this paper. To obtain more accurate degradation feature, a waveform matching extrema mirror extension EMD, which is used to suppress the end effects of EMD decomposition, was employed to decompose the original pump’s outlet pressure signals, taking the quasi-periodic characteristics of the signals into consideration. Subsequently, given that different failure modes of pumps have different degradation rates in practice, which makes it difficult to effectively recognize degradation status when using the modeling methods that need the normal and failure data, a Gaussian mixture model (GMM), which has no need for failure data when building a degradation identification model, was introduced to capture the new degradation status index (DSI) to quantitatively assess the degradation state of the pumps. Finally, the effectiveness of the proposed approach was validated using both simulations and experiments. It was demonstrated that the defined local instantaneous energy moment entropy is able to effectively characterize the degree of degradation of the pumps under variable operating conditions, and the DSI derived from the GMM is able to accurately identify different degradation states when compared with the previously published methods.