Thunderstorm downbursts are transient in nature and have been responsible for a variety of structural damages in recent years. Currently, the researchers have done several works on the characteristics of downburst wind speed. Nonetheless, rare attention has been placed on the structural aerodynamics characteristics subjected to downburst winds. Based on this, an experimental investigation is performed to reproduce downburst-like winds physically and to study the transient surface pressures (SPs) on a 5:1 rectangular cylinder (RC). The experiment is conducted within a multiple-fan active control wind tunnel (MFACWT) and mainly focuses on simulating the transient characteristics of downburst-like flow, including time-varying mean (TVM) wind speed and nonstationary wind fluctuation. The resulting SPs are measured to understand the influence of transient wind on the aerodynamic behavior of bluff bodies. The spatiotemporal characteristics of the SPs are analyzed using wavelet transform and Priestley's classic spectral theory. The results indicate that the transient nature of the downburst-like flow can be physically reproduced by a MFACWT. The instantaneous pressures of a RC are illustrated by both the turbulence parameters of the transient flow and the flow-separation characteristics. The pressure coefficients normalized by the TVM of the downburst-like winds remain constant, which provides a more appropriate way to estimate the transient gust loading in a quasi-steady manner. Interestingly, the phenomenon of the time-varying phase shift and time-varying correlation of chordwise SPs is observed when the turbulent velocity changes dramatically. In addition, the normalized surface pressure can be regarded as a stationary stochastic process, which provides a significant basis for further establishing the theoretical model of nonstationary gust-loading.