Fuzzy time series approach has been widely used to analyze real-world time series in recent years since using this approach has some important advantages. Various fuzzy time series models have been proposed in the literature in order to reach better forecasting results. A few of these models have been suggested to forecast seasonal time series and called as seasonal fuzzy time series. In this study, a new seasonal fuzzy time series forecasting model based on Markov chain transition matrix is proposed. In the proposed approach, fuzzy inference process is performed by using transition probabilities. Therefore, fuzzy time series approach proposed in this study is the first stochastic seasonal fuzzy time series method in the literature. To show the forecasting performance of the proposed method, it is applied to two real-world time series: the quarterly U.S. beer production and the number of foreign tourists visiting Turkey. As a result of the implementation, it is observed that the proposed method produces accurate forecasting results for both time series.