Aiming at the problem of extracting fault characteristic from changing-speed gearbox with compound faults, a compound faults diagnosis method for changing-speed gearbox based on order tracking demodulating spectrum is proposed. The rotate speed of changing-speed gearbox has the characteristic of time-varying, while the fault characteristic is always related to the rotate speed, and also has the characteristic of time-varying. In the proposed method, the rotate speed is estimated from original vibration signal by chirplet path pursuit algorithm. In order to transform the time domain non-stationary signal to the angular domain cyclostationary signal, the even angle resampling is carried out to the original signal according to the obtained rotate speed. The angular domain cyclostationary signal is analyzed by energy operator demodulating, and the compound faults diagnosis of changing-speed gearbox is executed according to the modulation information in the order tracking demodulating spectrum. The results, obtained by the analysis of algorithm simulation and application examples to the changing-speed gearbox with compound faults consisted of gear local fault and bearing local fault, show that the proposed method can effectively extract fault characteristic from changing-speed gearbox with compound faults under the condition of lack of tachometer.