The windowed synchronous averaging （WSA） is commonly applied to the fault detection of planetary structures since it can overcome the problem of time-varying transfer path. However，it is unsuitable for the fault feature extraction of the planet gear at the first stage in a two-stage planetary gearbox due to the vibration coupling caused by the two-stage planetary structures. To address the issue，an angle compensation synchronous averaging scheme is proposed in this paper. In the proposed scheme，the speed fluctuation of the observed vibration is eliminated by equal-angle resampling. The second-stage interference from the sun gear at the second stage is constructed by applying the synchronous averaging to the resampled vibration based on the angle compensation strategy. The second-stage interference is removed by subtracting it from the resampled vibration. The corresponding envelope signal is extracted by the envelope analysis from the residual vibration. The WSA is utilized to construct the synthetic envelope signal of the planet gear at the first stage. The envelope synchronous averaging is used to suppress the asynchronous interference and extract the fault feature of the planet gear. According to the experimental results of a two-stage planetary gearbox test rig，the effectiveness of the proposed method is verified.