Background: COVID-19 poses a severe threat to global human health, especially the USA, Brazil, and India cases continue to increase dynamically, which has a far-reaching impact on people's health, social activities, and the local economic situation. Methods: The study proposed the ARIMA, SARIMA and Prophet models to predict daily new cases and cumulative confirmed cases in the USA, Brazil and India over the next 30 days based on the COVID-19 new confirmed cases and cumulative confirmed cases data set(May 1, 2020, and November 30, 2021) published by the official WHO, Three models were implemented in the R 4.1.1 software with forecast and prophet package. The performance of different models was evaluated by using root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). Results: Through the fitting and prediction of daily new case data, we reveal that the Prophet model has more advantages in the prediction of the COVID-19 of the USA, which could compose data components and capture periodic characteristics when the data changes significantly, while SARIMA is more likely to appear over-fitting in the USA. And the SARIMA model captured a seven-day period hidden in daily COVID-19 new cases from 3 countries. While in the prediction of new cumulative cases, the ARIMA model has a better ability to fit and predict the data with a positive growth trend in different countries(Brazil and India). Conclusions: This study can shed light on understanding the outbreak trends and give an insight into the epidemiological control of these regions. Further, the prediction of the Prophet model showed sufficient accuracy in the daily COVID-19 new cases of the USA. The ARIMA model is suitable for predicting Brazil and India, which can help take precautions and policy formulation for this epidemic in other countries.