Coronaviruses are a huge family of viruses that affect neurological, gastrointestinal, hepatic and respiratory systems. The numbers of confirmed cases are increased daily in different countries, especially in Unites State America, Spain, Italy, Germany, China, Iran, South Korea and others. The spread of the COVID-19 has many dangers and needs strict special plans and policies. Therefore, to consider the plans and policies, the predicting and forecasting the future confirmed cases are critical. The time series models are useful to model data that are gathered and indexed by time. Symmetry of error's distribution is an essential condition in classical time series. But there exist cases in the real practical world that assumption of symmetric distribution of the error terms is not satisfactory. In our methodology, the distribution of the error has been considered to be two-piece scale mixtures of normal (TP–SMN). The proposed time series models works well than ordinary Gaussian and symmetry models (especially for COVID-19 datasets), and were fitted initially to the historical COVID-19 datasets. Then, the time series that has the best fit to each of the dataset is selected. Finally, the selected models are applied to predict the number of confirmed cases and the death rate of COVID-19 in the world.