The exponentiated Weibull (EW) distribution was introduced by Mudholkar and Srivastava(1993). This distribution is involving additional parameter to the Weibull distribution.  In this paper, we mainly estimate the three parameters of the exponentiated Weibull distribution using different methods of estimation such as: maximum likelihood method, method of moments, percentile estimation and least squares method. A comparison is performed based on variances, relative absolute biases, relative absolute estimate of risks and total deviation. The moment estimators are found to be appropriate than other methods. In addition, the sampling distributions of the moment estimators are obtained. A simulation study and concluding remarks are introduced.