In recent years, wearable sensor-based human activity recognition (HAR) is becoming more and more attractive, especially in health monitoring and sports management. However, in order to obtain high-quality HAR, it is often necessary to get sufficient labeled activity data, which is very difficult, time-consuming and costly in a natural environment. To tackle this problem, multi-source domain adaptation is a promising method that aims to learn enough multi-source prior knowledge from labeled activity data, and then transfer this learned knowledge to the target unlabeled dataset. Thus, this paper presents a novel multi-source weighted domain adaptation with evidential reasoning (w-MSDAER) for HAR, which can effectively utilize complementary knowledge between multiple sources. Specifically, we first use the strategy of distribution alignment to learn local domain-invariant classifiers based on multi-source domains. And then, the reliabilities of these derived classifiers are comprehensively evaluated according to the belief function based the technique for order preference by similarity to ideal solution (BF-TOPSIS). Finally, the discounting fusion method is used to fuse the local classification results. Comprehensive experiments are conducted on two open-source datasets, and the results show that the proposed w-MSDAER significantly outperforms other state-of-art methods.