A multi-stage surrogate model named LSTM-LFM-SRU was developed to address the high computational cost and limited real-time capability of traditional hydrodynamic models. The urban flood process was divided into two stages: one-dimensional drainage through pipe networks and two-dimensional surface inundation. Long short-term memory (LSTM) networks and a combination of a low-fidelity physical model (LFM) with a super-resolution U-shaped convolutional neural network (SRU) were adopted to replace the corresponding stages. A flood prediction framework was constructed by combining data-driven methods with physical information. The multi-stage surrogate model was applied to a case study in the Xiasha area of Hangzhou. A 20-hour intense rainfall-induced inundation event was simulated within 5.31, with its computational efficiency reaching 12.7 times that of the high-precision hydrodynamic models. The one-dimensional LSTM-based surrogate achieved an average Nash-Sutcliffe Efficiency value of 0.94, while the two-dimensional LFM-SRU model reduced the Root Mean Square Error by 17.2% compared with the LFM-U-net model.