The tremendous progress made in the field of deep learning allows us to accurately predict precipitation and avoid major and long-term disruptions to the entire socio-economic system caused by floods. This paper presents an LSTM–CP combined model formed by the Long Short-Term Memory (LSTM) network and Chebyshev polynomial (CP) as applied to the precipitation forecast of Yibin City. Firstly, the data are fed into the LSTM network to extract the time-series features. Then, the sequence features obtained are input into the BP (Back Propagation) neural network with CP as the excitation function. Finally, the prediction results are obtained. By theoretical analysis and experimental comparison, the LSTM–CP combined model proposed in this paper has fewer parameters, shorter running time, and relatively smaller prediction error than the LSTM network. Meanwhile, compared with the SVR model, ARIMA model, and MLP model, the prediction accuracy of the LSTM–CP combination model is significantly improved, which can aid relevant departments in making disaster response measures in advance to reduce disaster losses and promote sustainable development by providing them data support.