The development of bearing fault detection methods is of great significance for the performance maintenance of axial piston pumps. However, the reciprocating movement induced strong natural periodic impulses that completely submerged the fault characteristic frequencies of the axial piston pump. To solve this problem, a finite element method (FEM)-based band-pass filter method was proposed, combined with minimum entropy deconvolution. However, the performance is determined by the selected band-pass filter bandwidth and the pre-treated denoise techniques. In the present study, an improved version of the FEM-based band-pass filter method was developed by continuously changing the bandwidth of the filter. First, the central frequency was determined using the FEM-based band-pass filter method. Second, the bandwidths of the constructed band-pass filters were continuously changed with a certain incremental step to obtain multiple filtered signals from the raw signals. Third, the normalized Hilbert envelope spectra were collected from the filtered signals. Finally, the projection figure is obtained by automatically taking the spectrum lines with maximum amplitudes in the normalized Hilbert envelope spectra, and the fault features are further determined. The experimental results show that the bearing faults in the axial piston pump can be successfully detected using the proposed method. Compared to the original FEM-based band-pass filter method, the improved version does not require bandwidth selection of the band-pass filter and pre-treated denoising method.