In the era of satellite communication networks, driven by the evergrowing demand for connectivity and data exchange, the prediction of network traffic has emerged as a critical task. This has substantial implications for network management, anomaly detection, and the optimization of service quality. To address the challenges of forecasting network traffic in satellite communication systems, we introduce the Multi-Dimensional Spatio-Temporal Graph Convolutional Network (MDSTGCN), a novel model designed to capture the complex spatio-temporal dependencies inherent in satellite communication network data. The MDSTGCN leverages multi-dimensional graph convolutional neural networks to extract diverse network traffic features in space and time. It capitalizes on the distinct advantages offered by different adjacency matrices, thus achieving complementary effects and capturing implicit spatial relationships. The paper conducts experimental evaluations on datasets of network traffic and contrasts the outcomes with state-of-the-art models. The outcomes demonstrate the remarkable enhancements achieved by our proposed method in satellite communication network traffic prediction. By more accurately capturing temporal and spatial relationships among network nodes, our method elevates prediction accuracy and reliability.