This study investigates the cumulative damage of a 20-story high-rise steel building equipped with buckling-restrained braces (BRB) under the likely occurrence of earthquake and wind events in the design life of the building. The objective of this research is to introduce a method for evaluating the cumulative damage of BRBs under multi-hazard events that are expected to occur during the service life of a high-rise building in order to achieve a safer building. A methodology is proposed using a Poisson point process to estimate the timeline of earthquake and wind events, wherein the events are assumed to be independent in nature. The 20-story high-rise steel building with BRBs is designed according to the Japanese standard and analyzed using the finite element approach, considering nonlinearities in the structural elements and BRBs. The building is analyzed consecutively using the timeline of earthquakes and winds, and the results are compared with those under individual earthquakes and winds. In addition to the responses of the frame such as the floor displacement and acceleration, the damage of BRBs in terms of the damage index, the energy absorption, the plastic strain energy, and the maximum and cumulative ductility factor are evaluated. It is observed that the BRB’s fatigue life under multi-hazard scenarios is a multi-criteria issue that requires more precise investigation. Moreover, the overall building’s performance and BRB’s cumulative damage induced by the sequence of events in the design life of the building is significantly larger than that under an individual event.