According to Green Deal, the carbon neutrality of EU should be reached partly by transition from fossil fuels to alternative renewable sources. However, fossil fuels still play essential role in energy production, and are widely used in the world with no alternative to be completely replaced with, so far. In recent years we have observed rapidly growing prices of commodities such as oil or gas. The analysis of past fossil fuels consumption might contribute significantly to responsible preparation of energy policy of each country, reflected in policies of related organizations and industrial sector. Throughout years, there have been published a number of papers modelling production and consumption of fossil energy sources on the level of national economics, industrial sectors and households, exploiting and comparing a variety of approaches. In this paper, we model the consumption of fossil fuels in Slovakia based on annual data during the years 1965 - 2020. The Box-Jenkins methodology is used for analysis. Because of the presence of trend in the data, we consider autoregressive integrated moving average (ARIMA (p,d,q)) model. By fitting models with various combinations of parameters p, d, q, the best fitting model was chosen based on the value of Akaike’s information criterion. According to this criterion, the model for coal consumption is ARIMA(0, 2, 1) and for gas consumption ARIMA(2, 2, 2). With respect to these models, we might predict significant decrease in the coal consumption and almost constant consumption of gas in upcoming years in Slovakia.