A reasonable extreme probability model to estimate the transient loads is essential for structural wind resistance design. The transient aerodynamic characteristics of a 5:1 rectangular cylinder under thunderstorm-like wind are experimentally studied based on the multiple-fan active wind tunnel technique. In this paper, the non-Gaussian characteristics of the transient pressures are analyzed with emphasis on the time-varying skewness and time-varying kurtosis. A generalized time-varying extreme value model for uniformly modulated nonstationary stochastic processes is proposed, which is adopted to study the extreme value of transient loads on a 5:1 rectangular cylinder under a thunderstorm-like wind. Compared with the stationary flow condition, the results show that the non-Gaussian features of the transient pressures is noticeable, which is determined by the time-varying turbulence intensity. The greater the time-varying turbulence intensity, the stronger the non-Gaussian characteristic of the transient loads is, which is consistent with the stationary wind case. Notably, the presented work confirms that the conventional mean extreme value model may seriously underestimate the extreme value of transient loads. Moreover, the extreme values under stationary flow are slightly higher than those under transient wind pressures. The results show that the peak factors in the suction region are significantly greater than that in the reattachment region, and the time-varying peak factors under transient wind pressures are slightly less than in the stationary flow case.