Abstarct: In statistics, the analysis of regression is a practical method for investigating the relationships between one or some of response variables and a set of explanatory variables. The least squares method is one of the most commonly used methods for estimating regression coefficients. If all the assumptions of are true for a dataset, this method is the best estimator. But when it comes to observations of outlier data, this method is not a good prediction. In this case, robust regression methods are introduced as an alternative to classical methods. Furthermore if the observations are inaccurate too, the fuzzy robust regression are suggested. Fuzzy regression consists of two possible approaches and the least median squares. These methods are sensitive to outlier data. In this dissertation, the observations include outlier data. The exact explanatory variables and the response variables are fuzzy numbers. baxsed on the above assumptions, a robust fuzzy linear regression model baxsed on the least median of squares is represented. Then this method is combined to improve our estimation with the weighted least squares. The results from the examples show that the effect of the outlier data is neutralized or reduced.