To improve the construction performance and seismic resilience of precast reinforced-concrete frame structures, an innovative self-centering precast steel–concrete hybrid frame has been proposed and subjected to cyclic loading tests. In this paper, a comprehensive numerical analysis was conducted to further investigate the frame’s hysteretic behavior. Initially, a numerical model was developed using the finite element software OpenSees. Numerical analyses of two frame specimens were conducted, demonstrating good agreement between the numerical and experimental hysteretic characteristics, thus validating the model’s accuracy. Subsequently, based on the numerical simulations, a quantitative comparison of hysteretic performance between a novel frame and a traditional reinforced-concrete frame of the same scale was performed. While the proposed frame exhibited slightly lower initial stiffness and energy dissipation capacity than the traditional frame, it outperformed in terms of load-carrying capacity and self-centering ability. Finally, parametric analyses were carried out to assess the influence of various design parameters on the hysteretic performance, including friction force in the web frictions devices, initial post-tensioned force of the prefabricated steel–concrete hybrid beams, the steel arm length, and the column longitudinal reinforcement ratio. The results showed that increases in these four parameters improved the load-carrying capacity and initial stiffness of the proposed frame. Additionally, an increase in the friction force, steel arm length, or column longitudinal reinforcement ratio enhanced the frame’s energy dissipation capacity, while an increase in the initial post-tensioned force or a decrease in the friction force enhanced the frame’s self-centering capacity.