The concept of sponge cities is widely recognized, but there is still no research on what a new drainage system for sponge cities should look like. This study proposes a new drainage system for sponge cities, a sponge-type comprehensive pipe corridor rainwater chamber (SCRC) system, which combines a comprehensive pipe corridor with low-impact development measures (LIDs) into one system. The SCRC system is predicted by using a long- and short-term neural network to verify whether the neural network can be applied to the prediction of flooding in sponge cities. The results show that the SCRC system can effectively control sponge city flooding, where the surface runoff coefficient under different rainfall intensities (P = 1–10 yr) is between 0.273 and 0.44, the pipe overload time is between 0.11 and 3.929 h, and the node overflow volume is between 0 and 23.89 Mltr. The neural network has a high reliability in sponge city flood prediction, and the coefficients of determination R² of the test set of PSO–LSTM prediction models are all above 0.95. This study may provide an idea for predicting flooding in sponge cities.