In the density estimation it is known that estimators are heavily biased. We applied a bias reducing approach to improve some quantile estimators for Weibull distribution having different parameter values and contamination level. In this study, we estimate the bias for any quantile value and obtained biased reduced smoothed distribution function by simulation study for random samples of size 40. Then, the mean square error of some robust quantile estimators and variances are obtained from biased reduced smoothed distribution function. Furthermore, we obtained sampling distribution of roughness and sampling distribution of estimated bias related some quantile estimators.