This present study purposes to conduct Bayesian inference to estimate scale parameters, denoted by θ, with known location parameter or β, of Weibull distribution. There are two types of prior distributions used in this study, conjugate prior and non informative prior. As conjugate prior is inverse gamma, and as non-informative prior is Jeffreys' prior. This research also aims to study several theoretical properties of posterior distribution based on prior used implement it to generated data and make comparison between both Bayes estimator as well. The method used to evaluate as the best estimator is based on the smallest Mean Square Error (MSE) value. This study proveds that Bayes estimator using conjugate prior produces better estimated parameter value estimate non-informative prior since it produces smaller MSE value, for condition θ > 1 based on analytic and simulation study. Meanwhile for θ < 1 both priors could not yield acceptable estimated parameter value.