The new staggered story isolation structure is a novel seismic isolation structure developed from the base isolation structure and the inter story isolation structure. A large mainshock may trigger numerous aftershocks, which may cause greater damage to the structure. In this paper, the deformation and damage of the new staggered story isolation structure under the action of a single mainshock and mainshock aftershock sequences were analyzed. The finite element software ETABS for nonlinear time history response analysis was used to establish a 24 story frame core tube structure model. Results show that the damage on the core tube of the structure under mainshock aftershock sequences is concentrated between the frame isolation layer and the core tube isolation layer. The plastic hinge of the frame is concentrated below the frame isolation layer. The hysteretic curve of the corner column bearing of the frame isolation layer is full, and its energy dissipation effect is better than that of the core tube isolation layer. The maximum displacement of the isolation layer of the new staggered story isolation structure occurs in the frame isolation layer. Under the aftershocks, there is a significant increase in the damage to the new staggered floor isolation structure. Under aftershocks, the damage of the new staggered story isolation structure obviously increases. The damage to the frame part above and below the frame isolation layer increases by 8% and 10%, respectively, and the damage to the core tube increases by 19.80%. Aftershocks have a greater impact on the isolation layer, and the inter story displacement of the frame isolation layer and the core tube isolation layer increases by 78.70% and 60.54%, respectively.