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Tourism is one of the most significant and profitable sectors in Greece. It is a general truth because the tourism industry contributes to the economic prosperity and growth of the Gross Domestic Product (GDP) of our country. The importance and the magnitude of tourism in economy are constantly increasing and therefore it is vital for our country to be prepared to be able to predict tourism demand in the near future. In this research, various time series forecasting models are applied including Naïve models, ARMA, ARIMA and SARIMA. Furthermore, the increasing interest in Artificial intelligence has led to the utilization of some demonstrative AI models, for example, SVR, and then compared them to time series models. An attempt has been made with the view to comparing some time series models with the view to forecasting tourism demand in Greece. This paper aims to identify models, which estimate tourism demand in Greece with high performance. Τhe evaluation of the time series models was performed using accuracy measures such as, MAPE, MSE and RMSE. However, the findings of this study show up that besides simple Naïve method, the other four models provided a relatively good-performance but using different measure of each used model.