In this study, theoretical analyses are performed to investigate the characteristics of the static and dynamic stiffness of a nonlinear vibration isolator system. The vibration isolator system is modeled as an equivalent nonlinear oscillator. Based on the model, the static equilibrium and frequency response solutions are obtained with the variations of external static load and/or system parameters. It is shown that the static stiffness of the nonlinear vibration isolator tends to be hardened with the increase of external static load, which prevents the occurrence of excessively large deflection. This static stiffness-hardening effect is more remarkable with a larger spring constant ratio. The dynamic stiffness is also strengthened when the spring constant ratio increases, which enlarges the force transmissibility and reduces the isolation frequency bandwidth. Thus, the static stiffness- hardening improves the robustness of the nonlinear vibration isolator, whereas the dynamic stiffness-hardening rather degrades its performance. Thus, the opposite tendency of the static and dynamic stiffness-hardening effects should be considered in the design process of the nonlinear vibration isolator.