In this paper, we obtained Minimax estimator of the scale parameter for the Laplace distribution under the Squared log error loss function by applying the theorem of Lehmann [1950], and compared it with Minimax estimator under Quadratic loss function in addition of Maximum Likelihood Estimator according to Monte-Carlo simulation study. The performance of these estimators is compared depending on the mean squared errors (MSE’s). Keywords: Minimax estimator, Laplace distribution, Bayes estimator, Squared-log error loss function, Jeffery prior, Mean squared error
