With reference to the effect of the quadratic component of turbulent-wind fluctuation, the statistical moments of wind load up to the 4~(th) order are derived and the spectrum densities are given based on the Fourier transformation. By means of the Gram-Charlier series, the first-order probability densities of the structure responses are then constituted with the former 4~(th) order central moments of responses. Under the independent hypothesis of the structural displacement and its derivative, whose applicability is verified by the correlation between the two signals, the joint probability density function is developed and a numerical scheme for the analysis of the dynamic behaviors of the high-slender structure under wind excitation is obtained. Parametric analysis on dynamic responses and reliability under both Gaussian and non-Gaussian models of wind load are then investigated.