The purpose of this study is to study the spread of COVID-19, establish a predictive model, and provide guidance for its prevention and control. Considering the high complexity of epidemic data, we adopted an ARIMA-LSTM combined model to describe and predict future transmission. A new method of the ARIMA-LSTM model paralleling by weight of regression coefficient was proposed. Then, we used the ARIMA-LSTM model paralleling by weight of regression coefficient, ARIMA model, and ARIMA-LSTM series model to predict the epidemic data in China, and we found that the ARIMA-LSTM model paralleling by weight of regression coefficient had the best prediction accuracy. In the ARIMA-LSTM model paralleling by weight of regression coefficient, MSE = 4049.913, RMSE = 63.639, MAPE = 0.205, R2 = 0.837, MAE = 44.320. In order to verify the effectiveness of the ARIMA-LSTM model paralleling by weight of regression coefficient, we compared the ARIMA-LSTM model paralleling by weight of regression coefficient with the SVR model and found that ARIMA-LSTM model paralleling by weight of regression coefficient has better prediction accuracy. It was further verified with the epidemic data of India and found that the prediction accuracy of the ARIMA-LSTM model paralleling by weight of regression coefficient was still higher than that of the SVR model. In the ARIMA-LSTM model paralleling by weight of regression coefficient, MSE = 744,904.6, RMSE = 863.079, MAPE = 0.107, R2 = 0.983, MAE = 580.348. Finally, we used the ARIMA-LSTM model paralleling by weight of regression coefficient to predict the future epidemic situation in China. We found that in the next 60 days, the epidemic situation in China will become a steady downward trend.