To study the seismic performance of self-centering concentrically braced frame (SC-CBF) structure, the static elastoplastic analysis, low-cycle repeated loading analysis, and elastoplastic time-history analysis were conducted for a four-story SC-CBF structure, compared with the traditionally concentrically braced frame (CBF) structure. The influences of different GAP stiffnesses and cross-sectional areas of prestressed tendon were investigated on the self-centering and seismic performance of the SC-CBF structure. The results show that the SC-CBF structure has a strong lateral resistance, a small base shear under earthquake action, and a slight residual drift after unloading. The SC-CBF structure has a better ductility than the CBF structure. The displacement of the SC-CBF structure under the action of rare and extremely rare earthquakes is large, and the structure can dissipate more energy; the interstory drift is large, but the residual drift is small, exhibiting its ideal seismic and self-centering performance. However, the mechanical behavior of prestressed tendons is significantly affected by the stiffness of the GAP. The mechanical and seismic performances of the overall structure are slightly affected by the stiffness of the GAP, but the cross-sectional area of the prestressed tendons has a remarkable influence on the overall performance of the structure.