To investigate the seismic behaviors of novel steel-reinforced concrete composite frames prestressed with bonding tendons (PSRCFs), 15 groups of PSRCF specimens were designed with the following main parameters: the cubic compressive strength of high-strength concrete (fcu), the axial compression ratio of frame columns (n), the slenderness ratio of frame columns (β), the steel ratio of angle steel (α), the span–height ratio of frame beams (L/hb), and the prestressing degree (λ). Based on the modified concrete constitutive model proposed by Mander and the prestressing effect applied by the cooling method, the finite element models of PSRCFs were established by using ABAQUS software, the static analysis on the frame structures under the combined actions of axial forces and horizontal loads was carried out, and the monotonic load–displacement curves were explored. By comparing with the skeleton curves obtained by the experimental hysteretic curves, the rationality of the modeling method was verified. The PSRCFs had good mechanisms of strong columns and weak beams. Based on this, the influences of different parameters on the seismic behaviors such as hysteretic curves, skeleton curves, stiffness degradations, energy dissipation capacities, and ductility of the specimens were investigated. The results show that the hysteretic curves of the PSRCFs are full and have no pinch phenomenon. The ultimate load and the stiffness degradation of specimens can be improved significantly by increasing α, and on the contrary, the ultimate load and stiffness degradation decreased by increasing β. The ductility of the specimens decreased gradually with the increasing β and n. The energy dissipation capacity of the specimens decreased with the increasing β. The trilinear model of the skeleton curves and the restoring force model of PSRCFS were established by statistical regression, which agree well with the numerically simulated results. These can provide theoretical support for the elastoplastic analysis on this kind of PSRCF structure.