Sensor-based human activity recognition is important in daily scenarios such as smart healthcare and homes due to its non-intrusive privacy and low cost advantages, but the problem of out-of-domain generalization caused by differences in focusing individuals and operating environments can lead to significant accuracy degradation on cross-person behavior recognition due to the inconsistent distributions of training and test data. To address the above problems, this paper proposes a new method, Multi-channel Time Series Decomposition Network (MTSDNet). Firstly, MTSDNet decomposes the original signal into a combination of multiple polynomials and trigonometric functions by the trainable parameterized time series decomposition to learn the low-rank representation of the original signal for improving the extraterritorial generalization ability of the model. Then, the different components obtained by the decomposition are classified layer by layer and the layer attention is used to aggregate components to obtain the final classification result. Extensive evaluation on DSADS, OPPORTUNITY, PAMAP2, UCIHAR and UniMib public datasets shows the advantages in classification accuracy and stability of our method compared with other competing strategies, including the state-of-the-art ones. And the visualization is conducted to reveal MTSDNet's interpretability and layer-by-layer characteristics. Note to Practitioners-This paper is motivated by solving the problem of decreased classification accuracy caused by differences in human activity, such as the differences in walking patterns between young and elderly people. Models trained on young people's data are difficult to accurately recognize the activities of the elderly. This is a problem of domain generalization, where the distribution differences between training and testing data require the model's ability to generalize across domains. We propose a model based on time series decomposition, which helps the model learn universal features and effectively improve its generalization ability. This method can be further extended to time series tasks with varying domain distributions.