Regression models are a good tool for examining the relationship between response variable and one or more explanatory variables, that have a special place in statistics. A widely used regression model is quantile regression, that allows for the examination of explanatory variables effects across an entire response distribution and offer a fuller picture of the relationship between independent and dependent variables than that obtained by mean regression including ordinary least squares (OLS). Quantile regression estimators are not sensitive to outliers unlike OLS estimators. In other hand, quantile regression model does not require to specific hypothesis of OLS regression model, such as the normality of the response variable distribution and homogeneity of variance. Quantile regression is considered from both classical and Bayesian approach. Classical quantile regression is a nonparametric method in which no assumptions are made for model error distribution, but in the Bayesian framework, placing an asymmetric Laplace distribution on the error terms has attracted much attention.