Choosing the best subset is one of the key issues in formulating regression models. The purpose of these methods is to determine the predictor variables and to distinguish them from tolerable predictor variables so that the accuracy of the estimates and hence the accuracy of the future observations increases. When the number of the variables of the regression model is more than the number of the observations, or if there is a linear correlation between the predictors, choosing a variable with frequentist methods is usually inefficient and therefore the importance of Bayesian methods becomes more obvious. Among these methods, the Bayesian Lasso regression method is an appropriate choice, because by using this method we can compute the uncertainty level in any chosen model, however it is not the case in standard Lasso. Considering the fact that this method is sensitive to outliers, the convergence of the parameter estimation algorithm will decrease, therefore, it is better to use the robust methods. In this article, the Robust Bayesian Lasso regression is presented and its priority over the Bayesian Lasso regression will be mentioned.