Gas leakage and explosion accidents pose a serious threat to public safety. A critical prerequisite for accurately predicting the explosive effects of combustible gas leakage lies in determining the concentration distribution following the leakage. To develop a real-time, full-field spatiotemporal prediction model for combustible gas leakage and diffusion, and to achieve efficient prediction of the equivalent gas cloud volume, a novel graph neural network model based on a dual-neural-network architecture and a multi-stage training strategy, named multi-stage dual graph neural network (MSDGNN), was proposed. The MSDGNN model consists of two synergistic sub-networks: (1) a concentration network (N_con), which establishes the mapping relationship between the concentration fields of two consecutive timesteps, and (2) a volume network (N_vol), which generates the equivalent gas cloud volume at each timestep to provide a quantitative metric for explosion risk assessment. To further enhance model performance, a multi-stage progressive training strategy was developed to jointly optimize the dual networks. Experimental results demonstrate that compared with mesh-based graph network (MGN), the dual-network architecture effectively decouples the tasks of concentration field prediction and equivalent gas cloud volume prediction. This approach significantly mitigates the interference of weight factors in single-objective loss functions during the training process. The multi-stage training strategy, through stepwise parameter optimization, addresses the issue of insufficient data fitting encountered in traditional methods, significantly reducing the mean absolute percentage error ${\epsilon }_{\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}}$ for concentration fields and equivalent gas cloud volumes from 49.47% and 108.93% to 7.55% and 9.07%, respectively. Furthermore, the generalization error of MSDGNN for concentration fields and equivalent gas cloud volumes is reduced from 41.18% and 38.81% to 8.01% and 14.92%, respectively. In addition, MSDGNN exhibits robust prediction performance even when key parameters such as leakage rate, leakage height, and leakage duration exceed the range of training data. Compared with numerical simulation methods, the proposed model achieves a three-order-of-magnitude improvement in computational efficiency while maintaining prediction accuracy, providing an effective real-time analytical tool for combustible gas safety monitoring.