In this paper the Jeffery prior information and the extension of Jeffery prior information for estimating the parameter Weibull distribution is presented. Through simulation study the performance of this estimator was compared to the standard Bayes with Jeffery prior information with respect to the mean square error (MSE) and mean percentage error (MPE). In the results, The new estimator with extension of Jeffery prior information is the best estimator for Weibull Distribution, when compared it with standard Bayes with Jeffery prior information. Also depending on MSE and MPE, the is the best survival function for Weibull distribution when compared it with survival function based on posterior distribution. We can easily conclude that MSE and MPE of Bayes estimators decrease with an increased of sample size.