New low-damage seismic force-resisting systems have emerged after recognizing the need for resilient structures in severe earthquakes. Steel moment frames equipped with shape memory alloy (SMA) bolted connections provide a viable alternative to conventional steel moment frames to reduce structural damage, residual deformation, and repair costs. This paper applies performance-based design topology optimization to minimize the total cost of steel moment frames with SMA-bolted connections. A metaheuristic algorithm is used to perform topology optimization. The design variables are the cross-section of steel columns and beams, the properties of SMA connections, and the location of SMA connections. The practical, strength-related, strong-column weak-beam, Park-Ang damage index, and performance-based design constraints are considered in the optimization. The collapse capacity of the optimal designs is determined utilizing the FEMA-P695 methodology. Incremental dynamic analysis is performed, and fragility curves are generated to calculate the adjusted collapse margin ratios in assessing collapse safety. The performance-based design topology optimization is performed on 3- and 9-story steel moment frames with SMA connections. Optimal steel moment frames with SMA connections are compared to optimal conventional frames. The total cost of 3- and 9-story optimal steel moment frames using SMA connections are lower than those for conventional steel moment frames. Furthermore, optimal self-centering frames are found to provide acceptable collapse safety.