Single-source domain adaptation (SDA) methods are often used as traditional multi-source domain adaptation (MDA) methods. They aim to reduce the distance between the target domain and multiple source domains by aligning feature distributions. However, existing methods face challenges in pairwise feature alignment. Additionally, simply averaging the results of domain classifiers overlooks the differences in the impact of various source domains on the target domain. To tackle this issue, we suggest a multi-source domain adaptation algorithm called MADA that uses a cross-attention mechanism to evaluate the significance of each source domain. The algorithm then combines the outcomes of multiple domain classifiers through weighted aggregation. Additionally, a hybrid attention mechanism is employed to align domains and select transferable features. The experimental results demonstrate a significant improvement in the overall performance of the proposed network model compared to the baseline model. The accuracies achieved on the Office-31, Office-Home, and Hurricane datasets were 91.2%, 76.1%, and 93.0%, respectively.