The aim of this study is to estimate the volatility of oil prices and to determine the appropriate model and distribution for forecasting oil market volatility. For this purpose, the USD / barrel daily return series on Brent oil for the time periods from January 02, 2007 to December 31, 2016 are used in the study. To model oil price volatility, generalized autoregressive conditional heteroskedasticity (GARCH) models based on normal and student-t distributions and exponential GARCH (EGARCH) model, which is one of the asymmetric GARCH models that demonstrate the influence of positive and negative news on volatility are used. Error statistics are used to determine the most appropriate model between symmetric and asymmetric GARCH models. Analysis results suggest that GARCH (1,1) model based on student-t distribution performs better than symmetric and asymmetric GARCH models based on normal distribution in modelling the volatility of brent oil market