Earthquake events have shown that besides the earthquake forces, the interaction between the fault rupture and structures could cause a lot of damage. Field observations have revealed the need to design structures for fault-induced loading in regions with active faults. In this study, three-dimensional numerical simulation was carried out to evaluate the performance of a 20-story frame building subjected to the propagation of normal fault rupture. A parametric study was conducted with the propagation of the fault slip (h) with outcrop to the right (s/B=-1.0), at the mid (s/B=0.5), and left (s/B=2.0) of the raft. An advanced hypoplastic sand model (which can capture small-strain stiffness and stress-state dependent dilatancy of sand) was adopted. The Concrete Damaged Plasticity (CDP) model was used to capture the cracking behavior in the concrete beams, columns, and piles. The computed results revealed that the performance of the building due to the propagation of the normal fault rupture depends on the position of the outcrop of the rupture with respect to the building. Among the three simulated cases, the maximum differential settlement occurred when s/B= 0.5. In each case, the lateral movement of the building caused inter-story drift which may induce distress in the structural components of the building. The beams and the columns of the first story were fully damaged in tension when s/B was equal to -1.0 or 0.5.