A novel coronavirus was found in a seafood wholesale market in Wuhan, China. The World health organization (WHO) officially named this coronavirus as COVID-19. The disease had spread well outside China. An increase in confirmed cases is very high in the USA, UK, and Russia. Therefore, the purpose of the study was to forecast the number of infected cases in the USA, UK, and Russia. The daily confirmed cases of COVID-19 of the three countries for the period of 22nd January 2020 to 28th May 2020 were obtained from the WHO database. The Autoregressive Integrated Moving Average (ARIMA), Autoregressive Distributed Lag Models (ADLM), and Double Exponential Smoothing (DES) were tested. The Anderson–Darling test, Auto-Correlation Function (ACF), and Ljung-Box Q (LBQ)-test were used as the goodness of fit tests in model validation. The best-fitting model was selected by comparing relative and absolute measurements of errors. The ARIMA did not satisfy the model validation criterion for any of the countries, but the ADLM and DES did. It is concluded that the ADLM is the most suitable model for forecasting the USA and the DES is the best model for the UK. However, both models are equally good for Russia.