Unlike images and natural language tokens, time series data is highly semantically sparse, resulting in labor-intensive label annotations. Unsupervised and Semi-supervised Domain Adaptation (UDA and SSDA) have demonstrated efficiency in addressing this issue by utilizing pre-labeled source data to train on unlabeled or partially labeled target data. However, in domain adaptation methods designed for downstream classification tasks, directly adapting labeled source samples with unlabelled target samples often results in similar distributions across various classes, thereby compromising the performance of the target classification task. To tackle this challenge, we proposed a Global-Local Alignment Domain Adaptation (GLA-DA) method for multivariate time series data. Data from two domains were initially encoded to align in an intermediate feature space adversarially, achieving Global Feature Alignment (GFA). Subsequently, GLA-DA leveraged the consistency between similarity-based and deep learning-based models to assign pseudo labels to unlabeled target data. This process aims to preserve differences among data with distinct labels by aligning the samples with the same class labels together, achieving Local Class Alignment (LCA). We implemented GLA-DA in both UDA and SSDA scenarios, showcasing its superiority over state-of-the-art methods through extensive experiments on various public datasets. Ablation experiments underscored the significance of key components within GLA-DA.