Unsupervised domain adaptation methods aim to generalize effectively on unlabeled test data, which have a distribution shift from the training data, especially in the context of human activity recognition data with temporal dynamics. Achieving robust generalization is crucial for model performance. In this paper, we propose to incorporate uncertainty estimation into model training to enhance generalization and robustness. Specifically, we employ evidential learning for human activity recognition tasks, where a Dirichlet prior is imposed on the label to facilitate both target prediction and uncertainty estimation. The impact of the awareness of uncertainty is found to be crucial for domain adaptation, leading to better alignment of features between domains and significant performance improvements in the target domain. The uncertainty estimation quantitatively reflects prediction quality and characterizes the distance between the source and target domains. The uncertainty awareness model also demonstrates a much lower Expected Calibration Error (ECE) indicating a calibrated prediction confidence. Our experimental results demonstrate that the proposed method achieves state-of-the-art performances across multiple commonly used benchmark datasets using various baseline models, highlighting its effectiveness in the problems of unsupervised domain adaptation for human activity recognition. Our code is available at https://github.com/ZhongAobo/Evidential-HAR .