Gearbox bearings play an important role in wind power generation system. Their regular and stable operation will increase wind turbine power generation and improve the economic efficiency of wind farms. They often fail because they work under complex wind conditions. Therefore, it is necessary to find the fault early. The vibration signal of the gearbox bearing has the characteristics of volatility and continuity. Traditional bearing fault diagnosis methods are often based on signal analysis and feature selection, and the process is relatively complex. Deep learning methods can extract and select features automatically, thereby reducing the workload. A fault diagnosis method based on deep learning is proposed in this study. This method combines a one-dimensional convolutional neural network (1DCNN), support vector machine (SVM) classifier, and 1DCNN adaptively extracts features. The extracted features are input into the SVM classifier, and particle swarm optimization (PSO) is used to optimize the SVM classifier. The results show that the proposed fault diagnosis method is effective for fault diagnosis of wind turbine gearbox bearings. This method improves the precision and accuracy of diagnosis when compared to other methods.