The intrinsic mode confusion of empirical mode decomposition (EMD) and the ensemble empirical mode decomposition (EEMD) can only suppress mode confusion to a limited extent, as the white noise added by EEMD cannot be fully neutralized, which compromises the completeness of the original signal. Additionally, both methods fail to avoid interference from endpoint effects. Modal confusion and endpoint effects lead to distortions in the time-frequency analysis results obtained from the Hilbert transforms of EMD and EEMD. A complete ensemble empirical mode decomposition with adaptive noise and endpoint processing (EP-CEEMDAN) is proposed to address these issues. Simulation experiments were conducted to compare EMD, EEMD, and EP-CEEMDAN decomposition results on simulated vibration signals. Through multiscale permutation entropy detection and marginal spectral analysis, it was verified that EP-CEEMDAN has better control over endpoint effects and mode confusion, proving that EP-CEEMDAN is a more effective adaptive algorithm than EMD and EEMD. Finally, EP-CEEMDAN was applied to the processing of measured non-stationary vibration signals, where adaptive white noise was added at the endpoints of the vibration signals during each stage of decomposition. The method successfully generated various intrinsic mode functions (IMF) by calculating a unique residual signal. The EP-CEEMDAN algorithm effectively suppresses IMF endpoint divergence and modal confusion, while the time-frequency spectrum obtained through the Hilbert transform offers high resolution in both time and frequency domains. This result can be used for vibration feature recognition in non-stationary vibration signals.