When performing fault diagnosis tasks on bearings, the change of any bearing’s rotation speed will cause the frequency spectrum of bearing fault characteristics to be blurred. This makes it difficult to extract stable fault features based on manual or intelligent methods, resulting in a decrease in diagnostic accuracy. In this paper, a two-stage, intelligent fault diagnosis method (order-tracking one-dimensional convolutional neural network, OT-1DCNN) is proposed to deal with the problem of fault diagnosis under variable speed conditions. Firstly, the order tracking algorithm is used to resample the monitoring data obtained under different rotation speeds. Then, the one-dimensional convolutional neural network is adopted to extract features of the fault data. Finally, the fault type of collected data can be obtained by fully connected networks based on the features extracted. In the time domain, while the proposed algorithm only relies on the fault data collected under one speed as the training dataset, it is capable of doing fault diagnosis under different speed conditions. In the condition with the largest difference in speed with each dataset, the accuracy of the proposed method is higher than the baseline methods by 0.54% and 11.00%—on CWRU dataset and our own dataset respectively. The results show that the proposed method performs well in dealing with the fault diagnosis under the condition of variable speeds.