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It is expensive and time-consuming to collect sufficient labeled data to build human activity recognition (HAR) models. Training on existing data often makes the model biased towards the distribution of the training data, thus the model might perform terribly on test data with different distributions. Although existing efforts on transfer learning and domain adaptation try to solve the above problem, they still need access to unlabeled data on the target domain, which may not be possible in real scenarios. Few works pay attention to training a model that can generalize well to unseen target domains for HAR. In this paper, we propose a novel method called Semantic-Discriminative Mixup (SDMix) for generalizable cross-domain HAR. Firstly, we introduce semantic-aware Mixup that considers the activity semantic ranges to overcome the semantic inconsistency brought by domain differences. Secondly, we introduce the large margin loss to enhance the discrimination of Mixup to prevent misclassification brought by noisy virtual labels. Comprehensive generalization experiments on five public datasets demonstrate that our SDMix substantially outperforms the state-of-the-art approaches with 6% average accuracy improvement on cross-person, cross-dataset, and cross-position HAR.