Multivariate time series classification (MTSC) is vital across nume-ous real-world applications, requiring models that effectively capture complex spatio-temporal dependencies within high-dimensional data. Transformer-based architectures have recently established new performance benchmarks in MTSC by effectively modeling long-range dependencies. However, many existing models process spatial and temporal dependencies separately or integrate them only in later stages, thereby limiting their ability to fully exploit spatio-temporal correlations. Moreover, traditional attention mechanisms in Transformer exhibit quadratic computational complexity, hindering scalability and reducing effectiveness for large-scale MTSC tasks. In this paper, we introduce STLANet, a Spatio-Temporal Linear Attention Network, designed to address these challenges by fully integrating spatial and temporal dependencies throughout the model while significantly reducing computational complexity. STLANet incorporates an innovative Time Series Linear Attention (TSLAttn) mechanism that employs BiTransform activation and a local feature enhancement (LFE) approach to enhance feature expressiveness, resulting in more accurate and efficient attention computation. By utilizing distinct spatial and temporal embeddings in conjunction with a cross-attention mechanism, STLANet enables rich local and global spatio-temporal interactions, effectively capturing dependencies across various spatial and temporal levels. Experimental evaluations on 30 UEA MTSC datasets demonstrate that STLANet surpasses state-of-the-art models in classification accuracy with substantially lower computational costs. We believe that STLANet is a robust yet cost-effective approach to high-dimensional, large-scale time series analysis, and it provides a compelling solution for MTSC tasks in resource-constrained environments.