Having answered the question why the empirical frequency curve of annual extreme wind speeds at Tanggu, Tianjin of China does not fit the Pearson-Ⅲ type, the authors obtained a better fitting for the Weibull distribution through extremum analysis, and found out a better numerical solution for estimating the Weibull distribution parameters by a new iterative technique. The fitting results of annual extreme wind speed have been proved to be quite satisfactory by using the x2 criterion and Kolmogorov criterion.