The existing transfer learning-based fault diagnosis methods basically make use of fault knowledge learnt from one source domain to another target domain. Due to variable operating conditions, transfer tasks in the fault diagnosis need be inevitably performed many times, which limit their industrial applicability. To address the problem, a new residual deep subdomain adaptation network is proposed for intelligent fault diagnosis of bearings across multiple domains. Its remarkable advantage is that only one transfer task need be executed no matter how the operating conditions change. In this method, a residual network is constructed to extract transferable features from source domain and target domains. And, local maximum mean discrepancy is introduced to accurately align the distribution of the related subdomains within the same category in the source domain and the target domains. Comprehensive experimental results confirm that the proposed method can make use of fault knowledge learnt from the single source domain for fault diagnosis in the multiple target domains. The classification accuracy has a significant improvement as compared with the existing popular methods.