The gearbox is one of the key components of many large mechanical transmission devices. Due to the complex working environment, the vibration signal stability of the gear box is poor, the fault feature extraction is difficult, and the fault diagnosis accuracy makes it difficult to meet the expected requirements. To solve this problem, this paper proposes a gearbox fault diagnosis method based on an optimized stacked denoising auto encoder (SDAE) and kernel extreme learning machine (KELM). Firstly, the particle swarm optimization algorithm in adaptive weight (SAPSO) was adopted to optimize the SDAE network structure, and the number of hidden layer nodes, learning rate, noise addition ratio and iteration times were adaptively obtained to make SDAE obtain the best network structure. Then, the best SDAE network structure was used to extract the deep feature information of weak faults in the original signal. Finally, the extracted fault features are fed into KELM for fault classification. Experimental results show that the classification accuracy of the proposed method can reach 97.2% under the condition of low signal-to-noise ratio, which shows the effectiveness and robustness of the proposed method compared with other diagnostic methods.