Based on the theory of maximum likelihood estimation, a set of nonlinear equations is first derived for determination of parameters of Weibull distribution. To speed up convergence, an efficient algorithm is proposed for solving the parameters. Further, a large-span roof structure is taken to demonstrate the proposed method. It is proved that the responses of a nonlinear structure have non-Gaussian properties under the excitation of non-Gaussian stochastic wind pressure field. By Weibull distribution fitting, the maximum and minimum values of structural response with a certain assurance rate are computed, and the results are compared with those obtained from normal distribution.