Strong aftershocks have the potential to induce greater structural damage for Nuclear Power Plant (NPP) structures. In order to ensure the safety and integrity of Reinforced Concrete Containment (RCC) buildings, the base isolation technique is proposed to reduce the effects of earthquake shaking on the building and avoid damage of the structure under earthquakes. However, none of the studies have focused on evaluating the seismic performance of RCC buildings with isolation for mainshock-aftershock seismic sequences. The aim of this paper is to thoroughly investigate the structural damage of RCC buildings with Lead Rubber Bearing (LRB) isolators under seismic sequences. A suite of twenty-eight artificial sequential ground motions is developed to investigate the influence of considering aftershocks on the performance of RCC buildings with isolators for both design-basis and beyond-designbasis earthquake shaking. The results reveal that strong aftershocks would induce greater damage for the RCC without isolators under beyond-design-basis earthquake. While, base isolation can protect the RCC building under seismic sequences being damaged even for beyond-design-basis earthquake shaking. The IDA results of base-isolated RCC demonstrate that isolators also increase the structural reserve capacity significantly under both mainshocks and seismic sequences.