Recent studies have shown that Transformers perform well in multivariate time series forecasting (MTSF) tasks because of their excellent ability to capture long-term dependencies in sequences. However, the practice of channel mixing loses variable-specific information, leading to decreased prediction performance. Therefore, channel-independent structures have been widely adopted in recent MTSF tasks. Nonetheless, this approach neglects the dependencies between different variables in multivariate time series (cross-dimension dependency). Channel dependency is an inherent characteristic of MTS, and incorporating this property into the model can help more comprehensively model multivariate time series. To account for cross-dimensional dependencies under a channel-independent structure in Transformer-based models, this paper proposes a new model called BAGTST(representation token Block Attention Gated Time Series Transformer). Finally, extensive experimental results on 7 widely-used real-world datasets demonstrate that BAGTST achieves stable performance improvements compared to state-of-the-art models.