Multivariate time series classification (MTSC) plays a critical role in a wide range of real-world applications, such as healthcare, finance, and industrial monitoring. This paper proposes a triple-fusion network (TriFusNet), a novel convolutional network designed to address the challenges of MTSC. TriFusNet employs a specialized architecture that captures both variable-specific features and features shared across variables through the parallel use of standard, depth-wise, and shared-kernel convolutions. A hierarchical triple-fusion strategy is introduced to enhance representation learning across three stages: input-level fusion transforms raw variables, intermediate-level fusion integrates heterogeneous features, and output-level fusion improves decision robustness. Extensive experiments on 26 benchmark datasets show that TriFusNet outperforms 15 competitive baselines, achieving the best average rank (4.3077) with a Win/Draw/Loss of 5/4/17. The effectiveness of its architectural design and parameter settings is empirically validated, and a qualitative theoretical discussion is conducted to support the proposed fusion strategy. These results highlight TriFusNet's strong potential for real-world applications involving complex and high-dimensional time series data.