Single-rod magneto-rheological dampers (MRD) have the advantages of a simple mechanism, high reliability, and broad application range. They are widely used in various semi-active vibration control fields. However, their working mode requires a compensating mechanism to perform volume compensation on the rod, leading to additional stiffness for the system. Ignoring this point makes it tough to establish an accurate mechanical model to describe its performance in the design stage, affecting its application. To address this issue, this study proposes a multi-physics simulation model based on gas compensation for single-rod MRD to characterize their mechanical performance accurately. Firstly, the mechanism and mechanical model of the single-rod gas compensation MRD are introduced. Secondly, considering that its performance is affected by the coupling effect of multiple physical fields, including magnetic, flow, and solid mechanics fields, the control equations and boundary conditions of each field are analyzed separately, and a multi-physics coupling simulation model is established by COMSOL. In particular, the gas compensation unit is considered in the multi-physics simulation model. The effect of the compensating mechanism on the mechanical performance of the damper under different excitation speeds, currents, and initial pressures is analyzed. Finally, the accuracy of the proposed method is verified through the demonstration power test. The results show that the simulation can describe the additional stiffness in the damper. The average error between experimental value and simulation value is 7%. This demonstrates the degree of agreement between the experiment and simulation.