Recently, significant progress has been made in the field of multivariate long-term time series forecasting using Transformer-based methods. However, these methods often incur high computational complexity during attention computation, and most Transformer-based approaches neglect targeted modeling of local features. To solve these problems, this paper proposes a Multi-scale Convolutional Intermediary Attention Network (MCIAN). Modeling both local and global correlation features of the time series is considered to comprehensively capture the overall view of the time series. MCIAN utilizes multiple branches of convolutional neural networks to capture different local patterns of time series and adopts an intermediary attention mechanism to model the global correlation of time series. In order to make the output features closer to the target sequence, this paper uses a gating unit to screen the output features of multiple branches. In addition to exhibiting higher results in terms of performance, our method achieves a computational complexity that is linearly proportional to the length of the sequence. Experimental results on six public datasets show that our method outperforms the state-of-the-art baselines.