Since the Weibull distribution has been accepted reference distribution in wind energy field, topics on its parameter estimation methods have been attracted issue. In this context, the literature have generally focused on non-robust methods which may yield questionable results in the cases of unusual and contaminated wind speed data. This paper discusses some robust estimation methods of the Weibull distribution for unusual wind speed data cases. The considered robust methods are evaluated by using artificially generated unusual wind speed data cases. It was found that some of the considered robust methods provide reliable results compared classical ones. Also, the same results are observed for the estimation of mean power density error. As a result, analyzes performed shows that robust and efficient classical methods can be used together to check results.