In this paper, COVID-19 cumulative cases are estimated with AKF based on total COVID-19 cases between January-September 9, 2020 in USA, Germany, United Kingdom, Italy, France, Russia, Brazil, India, Turkey, Spain, Peru, Colombia, South Africa, Argentina, Iran, Pakistan. The cumulative covid-19 cases time-series was modeled with a stochastic dynamic linear model (DLM). The estimation performance of the models is measured by the calculation of mean square error (MSE) and coefficient of determination ( ). Calculated MSE and values showed that the model and AKF could be used to estimate the number of cases in these countries. In this study, firstly, the cumulative number of cases was estimated. Secondly, using these estimates number of daily cases was calculated. Thirdly, the reproduction number was obtained by using these number of daily cases. The model and estimation method used is suitable. The AKF algorithm uses only the number of cases in the last day. We propose that the model and estimation method under consideration is a convenient tool for calculating the reproduction number depending on time.