Condition monitoring and fault diagnosis of the planet bearing is key to operational reliability of the planetary gearbox, and also have remained challenging due to complex modulation phenomenon and strong planetary gear noise. As such, a new fault diagnosis strategy based on the synchrosqueezing transform (SST) and the deep convolutional neural network (DCNN) is proposed in this paper. Specifically, the envelope time-frequency representations (TFRs) of the vibration signals of the planetary gearbox are firstly calculated using the Hilbert transform and the SST. Next, a DCNN is constructed to learn the underlying features from the TFRs and then the fault types can be determined automatically. As its main contribution, the proposed method automatically recognizes the planet bearing fault type, which is free from artificially capturing fault characteristic frequencies in spectrum or time-frequency spectrum that contain many interference items, and effectively avoid missed diagnosis and misdiagnosis. In addition, it is also free from considering frequency band selection, which is difficult duo to the strong interferences of the gear meshing vibration. The analysis results of the planetary gearbox data demonstrate effectiveness of the proposed approach with a classification accuracy better than 98.3%.