The influence of the damper support stiffness on the damping effect of suspension bridge hangers was studied by means of numerical method. Firstly, governing equations of the support-damper-hanger system were established by simplifying the damper support as a spring-oscillator model. Secondly, the discontinuous Dirac Function in the governing equations was approximately handled to adapt the Finite Difference Method (FDM) utilized in this paper, and the governing equations of the support-damper-hanger system were numerically solved by FDM. The effect of the damper stiffness on the dimensionless curve of damping ratio, realizable maximum damping ratio and its corresponding damping coefficient, as well as mass of damper support was carefully studied. The results obtained in this paper agree well to the literature results. The results also show that the realizable maximum damping ratio and its corresponding optimal damping coefficient decrease with the decrease of the damper support stiffness, which affects the efficiency of the damper. As the dimensionless curves related to the damping ratio exhibit obvious differences at each mode, it is impossible to use a Universal Curve related to modal damping ratio to design the damper parameters. In addition, the mass of the damper support has little influence on the damping ratio.