Abstract: Recently, multivariate time series (MTS) forecasting techniques have seen rapid development and widespread applications across various fields. Transformer-based and GNN-based methods have shown promising potential due to their strong ability to model interaction of time and variables. However, by conducting a comprehensive analysis of the real-world data, we observe that the temporal fluctuations and heterogeneity between variables are not well handled by existing methods. To address the above issues, we propose CrossGNN, a linear complexity GNN model to refine the cross-scale and cross-variable interaction for MTS. To deal with the unexpected noise in time dimension, an adaptive multi-scale identifier (AMSI) is leveraged to construct multi-scale time series with reduced noise. A Cross-Scale GNN is proposed to extract the scales with clearer trend and weaker noise. Cross-Variable GNN is proposed to utilize the homogeneity and heterogeneity between different variables. By simultaneously focusing on edges with higher saliency scores and constraining those edges with lower scores, the time and space complexity (i.e., $O(L)$) of CrossGNN can be linear with the input sequence length $L$. Extensive experimental results on 8 real-world MTS datasets demonstrate the effectiveness of CrossGNN compared with state-of-the-art methods.