Abstract: A series of single-degree-of-freedom semi-active nonlinear vibration isolation system with cubic stiffness based on relative velocity feedback on-off control is studied. By using the averaging method, the approximate analytical solutions of the primary resonance of the system are obtained, which is controlled by the acceleration and relative velocity based acceleration drive damping control, the velocity and relative velocity based sky-hook damping control, and the displacement and relative velocity based ground-hook damping control, respectively. A further comparison between the numerical solutions and the approximate analytical solutions under different control strategies is fulfilled. And such comparison results suggest that the approximate analytical results are quite consistent with the numerical solutions, which verifies the effectiveness of the approximate analytical solutions. Moreover, the stability conditions of the steady-state solution of the system under different control strategies are analyzed by Lyapunov theory, and the influences of system parameters on the control effect are discussed. In order to compare the control performances in the three different control approaches, the amplitude-frequency response equation is conducted. The results show that the similar expressions can be found in the switching conditions in the process of the analytical analysis of the three relative velocity feedback control strategies. In the aspect of suppressing resonance response amplitude, the sky-hook damping control strategy based on velocity and relative velocity feedback has the best damping effect in low frequency band, while the acceleration drive damping control strategy based on acceleration and relative velocity feedback has the best damping effect in high frequency band. The sky-hook damping control strategy also shows good performance in reducing the amplitude response of transient response. This analytical research method can also be applied to the system with other semi-active on-off control strategies, and it provides an effective way for the control strategy research of semi-active vibration isolation system.