A method of combining auto-correlation and Hilbert envelope analysis is proposed and used to identify weakness imbalance fault of aero-hydraulic pump, the central part of hydraulic system of aircraft. Firstly, the integral and polynomial least square fitting is applied to convert acceleration signal to velocity one; secondly, the Hilbert envelope spectrum of auto-correlation function of velocity signal is obtained and used to identify the weakness imbalance fault of aero-hydraulic pump; finally, the energy ratio of velocity signal is calculated according to Hilbert envelope spectrum for identifying imbalance fault of aero-hydraulic pump by means of easier and more visual method. Meanwhile, the comparing analysis is carried out between traditional research method and proposed new one. The result shows that the weakness imbalance fault of aero-hydraulic pump can be identified and diagnosed effectively and correctly according to the velocity signal whether Hilbert envelope spectrum or calculation energy ratio while direct acceleration signal cannot.