Various types of Coronaviruses are enveloped RNA viruses from the Corona-viridae family and part of the Coronavirinae subfamily. This family of viruses affects neurological, gastrointestinal, hepatic, and respiratory systems. Recently, a new memb-er of this family, named Covid-19, is moving around the world. The expansion of Covid-19 carries many risks, and its control requires strict planning and special policies. Iran is one of the countries in the world where the outbreak of the disease has been serious and the daily number of confirmed cases is increasing in some places. Prediction of future confirmed cases of the COVID-19 is planning with a certain policy to provide the clinical and medical supplementary. Time series models based on the statistical methodology are useful to model and forecast time-indexed data. In many situations in the real world, the ordinary classical time series models based on the symmetrical and light-tailed distributions cannot lead to a satisfactory result (or predicion). Thus, in our methodology, we consider the analysis of symmetrical/asymmetrical and light/heavy-tailed time series data based on the two-piece scale mixture of the normal (TP-SMN) distribution. The proposed model is useful for symmetrical and light-tailed time series data, and it can work well relative to the ordinary Gaussian and symmetry models (especially for COVID-19 datasets). In this study, we fit the proposed model to the historical COVID-19 datasets in Iran. We show that the proposed time series model is the best fitted model to each dataset. Finally, we predict the number of confirmed COVID-19 cases in Iran.