There are complex risk correlations between financial sectors, and the risks generated by different financial sectors propagate, accrue, and cluster through the network of correlations, posing a threat to the entire financial system. This research constructs static and dynamic cross-sector risk spillover networks using VAR and generalized variance decomposition, and forecasts the evolution of risk spillover networks using recurrent neural network models such as RNN and LSTM. The results indicate that the risk spillover network will change rapidly in response to risk events, and that the total volatility spillover will increase during times of crisis, while banks and securities are the most important risk propagating and receiving sectors. The LSTM model can achieve more effective dynamic prediction of the multidimensional network, and the predicted network is essentially consistent with the actual network. According to the findings of the study, forecasting changes in the structure of financial sector networks may provide early warning of systemic financial risk and assist to a better understanding of the risk link between financial sectors.