For the variable speed condition， the vibration signal of the gearbox is characterized by non-stationary， strong interference and signal modulation， which make the rolling bearing fault difficult to be accurately diagnosed. Therefore， a fault envelope order spectrum analysis method with fast kurtogram for rolling bearings is proposed. The fast kurtogram is used to adaptively determine the filtering parameters， meanwhile， the time domain signal is bandpass filtered and enveloped to improve the signal-to-noise ratio. Furthermore， the time domain non-stationary signal after the envelope is resampled and converted into an angular pseudo-stationary signal to eliminate the “frequency ambiguity”. Finally， the spectral analysis of envelope signal in the angular domain is used to obtain the order envelope spectrum， and the fault diagnosis of rolling bearing is realized by comparing with order features. The simulation and signal analysis experiments of the outer ring fault of the gearbox rolling bearing during the speed increases from 600~1 500 r/min are completed. The experiment results show that the proposed method has a maximum fault error order of 1.84%， which can effectively extract the fault characteristics of rolling bearings under variable speed conditions and judge the fault types of them.