Deep neural networks often experience performance degradation when evaluated on testing (target) data that exhibit different distributions compared to the training (source) data. To solve the issue, Domain Generalization (DG) approaches were proposed by researchers to learn models that demonstrate robustness to domain shift. These models were trained on the data from source domains without accessing data from the target domains. Besides, the existing Normalization-based DG methods capture augmented and original styles through a single deep learning model, hindering the effective learning of these distinct style variations. Therefore, to effectively learn the augmented styles while preserving the original styles of source domains, a novel framework called Collaborative Learning with Normalization Augmentation (CLNA) is proposed for time series data in this paper. To validate the superiority of our proposed framework, CLNA was compared to seven state-of-the-art methods on three publicly available time series datasets. These experiments were conducted for both single-source and multi-source Domain Generalization problems. Experimental results showed that CLNA achieves significantly improved classification accuracy compared to existing approaches.