Due to their high transmission ratio, high load carrying capacity and small size, planetary gears are widely used in the transmission systems of wind turbines. The planetary gearbox is the core of the transmission system of a wind turbine, but because of its special structure and complex internal and external excitation, the vibration signal spectrum shows strong nonlinearity, asymmetry and time variation, which brings great trouble to planetary gear fault diagnosis. The traditional time-frequency analysis technology is insufficient in the condition monitoring and fault diagnosis of wind turbines. For this reason, we propose a new method of planetary gearbox fault diagnosis based on Compressive sensing, Two-dimensional variational mode decomposition (2D-VMD) and full-vector spectrum technology. Firstly, the nonlinear reconstruction and noise reduction of the signal is carried out by using compressed sensing, and then the signal with multiple degrees of freedom is adaptively decomposed into multiple sets of characteristic scale components by using 2D-VMD. Then, Rényi entropy is used as the optimization index of 2D-VMD analysis performance to extract the effective target intrinsic mode function (IMF) component, reconstruct the dynamics signal in the planetary gearbox, and improve the signal-to-noise ratio. Then, using the full-vector spectrum technique, the homologous information collected by numerous sensors is data layer fused in the spatial domain and the time domain to increase the comprehensiveness and certainty of the fault information. Finally, the Teager–Kaiser energy operator is used to demodulate the potential low-frequency dynamics frequency characteristics from the high-frequency domain and detect the fault characteristic frequency. Furthermore, the correctness and validity of the method are verified by the fault test signal of the planetary gearbox.