The rapid spread of Corona Virus Disease 2019 (COVID-2019) has seriously threatened people’s health and brought huge challenges to the medical systems of many countries. So it is necessary to predict the epidemic trend scientifically and accurately. In this paper, the development trend prediction of the global daily cumulative confirmed case, based on data from February 2, 2020 to August 14, 2021 using linear regression and nonlinear regression methods, which are auto regressive integrated moving average (ARIMA), wavelet neural network (WNN), support vector machine (SVM), recurrent neural network (RNN) and long short-term memory (LSTM). Mean Absolute Error (MAE), Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE) were used to evaluate the prediction accuracy of the five models. The experimental results showed that the LSTM used in this study is more accurate for predicting the development trend of global cumulative confirmed cases. And its three evaluation indexes were 0.0936%, 0.1123%, and 0.0962% respectively, which were the smallest compared with the other four models. The LSTM model was used to predict the global cumulative confirmed cases in the next five days. The prediction results showed that the global cumulative confirmed cases will rise steadily and exceed 205 million. Therefore, the health departments of various countries should take appropriate prevention and control measures in advance.