Transfer learning-based fault diagnosis has received intensive attention from researchers. Under various working conditions, high-precision cross-domain fault diagnosis remains a problem due to distribution differences between different source domains and between source and target domains. Therefore, reducing the distribution difference between source domain and target domain data is crucial for improving the model's ability to learn domain-invariant features and fault-representative features. To address this challenge, this paper proposes a multi-source adversarial domain adaptation approach for fault diagnosis, referred to as MSD-MCA, which is based on the alignment of multiple classifiers. The method constructs a sub-network for each source domain and utilizes domain adversarial training to extract domain-invariant features. It then generates a fault feature set for each source domain by leveraging the domain-invariant features corresponding to various fault types. To align the target domain with the source domains, the Wasserstein distance is calculated between the target features and each fault feature set. Minimizing the entropy of the distribution distance vector facilitates the learning of fault-representative features. Additionally, an association matrix is employed to enhance the stability of the decision boundaries during the training process. This approach improves the model's capacity to generalize across multiple domains while effectively capturing fault-related information. To validate the efficacy of the proposed MSD-MCA method, a comparative analysis was conducted against several state-of-the-art diagnostic approaches. The evaluation was performed on bearing fault data from Case Western Reserve University, as well as two real-world industrial datasets. The results indicate that MSD-MCA shows improved accuracy and enhanced generalization capabilities across both datasets. Consequently, MSD-MCA can better learn the domain-invariant features and fault-representative features and improve the accuracy of fault diagnosis.