Sequential data plays a pivotal role in various real-world applications, such as traffic flow and source code, and is characterized by its strong temporal dependencies. Although deep neural networks (DNNs) achieve promising performance in sequential data analysis, they usually require large amounts of labeled data. Multi-source domain adaptation (MSDA) alleviates this issue by transferring knowledge from multiple source domains to the target domain. However, existing MSDA methods often ignore temporal dependencies and adaptive domain relevance in sequential data. To address these limitations, this paper proposes MSDA4SD, a multi-source domain adaptation framework based on long short-term memory (LSTM) networks and a domain-correlation attention-based weighted maximum mean discrepancy (WMMD) mechanism. MSDA4SD captures temporal features while adaptively aligning source and target domain distributions to improve robustness and generalization. Experiments on vulnerability multi-classification and traffic flow prediction datasets demonstrate that MSDA4SD consistently outperforms existing MSDA methods. Specifically, MSDA4SD improves the average Accuracy by 0.3%–0.6% in vulnerability multi-classification tasks, reduces MAE by 10.2%–19.4%, and decreases RMSE by 8.7%–16.9% in traffic flow prediction tasks.