Lithium-ion battery NMC cathode materials possess high specific capacity and energy density, with their macroscopic electrochemical performance being significantly influenced by the microstructure. However, in the FE2 framework, modeling polycrystalline microstructure at the microscale with a cohesive phase field damage model leads to a substantial increase in computational cost. Traditional data driven surrogate models are often black box in nature and lack interpretability, while neural network models incorporating convolutional operations tend to extract features that are too abstract to correlate with specific physical mechanisms. Graph Neural Networks (GNNs) can effectively represent polycrystalline microstructures as graph structures and clearly characterize physical features such as grain area, grain orientation, and grain boundary parameters, making them well-suited for constructing surrogate models of polycrystalline microstructures. This study focuses on developing a GNN based surrogate model for polycrystalline microstructures and coupling it with a macroscopic performance model to establish a GNN based multiscale surrogate modeling framework. This framework aims to investigate the influence of variations in microstructural parameters on macroscopic battery performance, providing theoretical insights for the design and optimization of microstructures and thereby contributing to the enhancement of battery performance.