In light of the aliasing of vibration signals, and the incipient fault features covered by stronger harmonic components at different levels and environmental noise, a fault diagnosis approach is proposed for planetary gearboxes using a multi-resonance component fusion-based convolutional neural network (MRCF-CNN). First, the vibration signal is decomposed using resonance-based signal sparse decomposition (RSSD) for the high resonance components containing the harmonic components of the gears and the low resonance components that may contain the impulse components of bearing faults. Then, a convolution neural network with multi-resonance component fusion is constructed from which the obtained high and low resonance components are adaptively fused with the original vibration signals at the feature level. Finally, the supervised model is trained to diagnose the faults of planetary gearboxes. The experimental result shows that the proposed method can classify failures of rolling bearings and gears in planetary gearboxes, diagnose the planetary gearbox failure, and enhance the ability of convolution neural networks to detect fault information from vibration signals.