Modeling data of extreme values, i.e., the highest and lowest values of natural phenomena by statistical formulas, makes it possible to predict the behavior of such data in the future. One of the methods of analyzing extreme values is the exceedances method, in which all the exceedances over a high threshold are modeled using the generalized Pareto distribution. In this paper, using this method, the statistical model is fitted to the data of high values and low values of temperature of Tabriz city in the period of 1951 to 2020, the parameters of the model are estimated, the goodness of fit of the model is evaluated, and finally some necessary predictions such as the mean return periods of minimum and maximum values of the temperature of Tabriz have done for different periods of time. One of the results of this study is that with 95% confidence, the upper limit for the maximum temperature of Tabriz is equal to 41.11 ° C with an average return period of 20 years and the lower limit for the minimum temperature of Tabriz is equal to -20.91 ° C with the average return period of 20 years.