Based on the prediction of hospital inpatients, first Prophet model and long- and short-term memory (LSTM) recurrent neural network prediction method were used to design a combined prediction model based on particle swarm optimization (PSO). Both Prophet and LSTM neural network models were used to simulate and analyze the time series data of the inpatients of respiratory medicine in Shanghai Oriental Hospital from January 2015 to December 2019. Then the particle swarm algorithm was used to find the corresponding combination coefficients of the two models to obtain the final Prophet-LSTM-PSO combined model. By the RMSE and MAE statistical indicators, the combined model was compared with the single model. At the same time, comparative experiments were carried out with open datasets. Results show that Prophet-LSTM-PSO combined model can effectively reduce prediction deviation and improve prediction accuracy compared with single models including Prophet, LSTM, and autoregressive integrated moving average model (ARIMA).