Stock market prediction has been a key topic in finance. In this study, we design a deep graph neural network model to integrate the correlation structure and attention mechanism of financial markets to realize volatility prediction. The experimental data covers CSI 300 constituent stocks from 2018 to 2023, and day-level trading data is used to verify the model performance. The test results show that the model achieves 78.9% directional accuracy with an RMSE of 0.0182, which is a 23.5% improvement over traditional methods. The prediction accuracy stays above 75.8% during typical stock market volatility periods. The experiment proves that the graph neural network model has a good application prospect in the field of financial market prediction and provides data support for quantitative investment decision making.