Bearing fault diagnosis plays a vitally important role in practical industrial scenarios. Deep learning-based fault diagnosis methods are usually performed on the hypothesis that the training set and test set obey the same probability distribution, which is hard to satisfy under the actual working conditions. This paper proposes a novel multilayer domain adaptation (MLDA) method, which can diagnose the compound fault and single fault of multiple sizes simultaneously. A special designed residual network for the fault diagnosis task is pretrained to extract domain-invariant features. The multikernel maximum mean discrepancy (MK-MMD) and pseudo-label learning are adopted in multiple layers to take both marginal distributions and conditional distributions into consideration. A total of 12 transfer tasks in the fault diagnosis problem are conducted to verify the performance of MLDA. Through the comparisons of different signal processing methods, different parameter settings, and different models, it is proved that the proposed MLDA model can effectively extract domain-invariant features and achieve satisfying results.