In previous earthquakes, many steel frames suffered damage to their ordinary rigid moment beam-to-column connections. As a result, the use of multi-level control systems in structures has gained attention from engineers in recent years. The main idea in this system is to combine two separate control systems with different stiffness and strength, thus creating dual seismic behaviors. In this study, a two-level friction-yielding damper passive control system is presented for beam-to-column connections, and its cyclic behavior is evaluated using nonlinear static analysis with the finite element method using ABAQUS software. The evaluation results demonstrate that the performance of the samples improves with an optimal ratio of length to thickness. This improvement is reflected in increased stability and area of the hysteresis curves, ultimately leading to higher energy absorption. Additionally, the hysteresis curves indicate a ductile behavior for the proposed damper in the moment connection. Moreover, the obtained hysteresis curves show that the system reliably dissipates energy at different earthquake levels, satisfying the seismic criteria for special moment resistant connections based on the AISC code. The proposed damper serves as an energy dissipating device, effectively dissipating energy at different levels of earthquakes by facilitating slip and yielding, thereby controlling the seismic response of the structure.