Tropical cyclones could cause co-occurrences of storm tides and rainfall and, therefore, induce flooding hazards, posing high risks to coastal cities. Accurate and timely prediction of flood hazards in time–space domain is essential for flood risk management. In this study, a hybrid surrogate model is proposed for real-time flooding prediction by considering the compound effects of storm tides, rainfall, and drainage outflows. The hybrid surrogate model combines a long short-term memory (LSTM) neural network for predicting drainage outflows with a one-dimensional convolutional neural network (1D CNN) for predicting water depths. The model is tested using performance metrics, and the simulation results agree well with the historical measurements. Moreover, a sensitivity analysis of the drainage outflows using the modified Morris screening method reveals the importance of considering drainage systems in flood modelling, particularly when rainfall return periods are relatively small. The sensitivity indices vary over the computation domain in terms of different driving factors, with positive values corresponding to rainfall-dominated area while negative values corresponding to storm tide-dominated area. The computation cost of the model is quite low, and the fast prediction speed could provide a sound basis for early warning and real-time flood management. The proposed hybrid surrogate model offers a promising function for rapid and accurate flood inundation prediction in coastal cities, enabling more effective flood risk management and emergency response planning.