Abstract: The 1/3 subharmonic resonance of the quasi-zero-stiffness nonlinear vibration isolation system with dry friction damper is studied by using the incremental averaging method, which is subjected to external simple harmonic excitation. Firstly, the approximate analytical solution of the primary resonance of the quasi-zero-stiffness vibration isolation system with dry friction damper is obtained by using the averaging method. Then, based on the approximate analytical solution of the primary resonance of the system, the subharmonic resonance response of the system is regarded as an increment, and the approximate analytical solution of the subharmonic resonance of the quasi-zero-stiffness vibration isolation system is obtained by using the averaging method. The stability conditions of the steady-state solutions of the primary resonance and subharmonic resonance of the quasi-zero-stiffness vibration isolation system are obtained by using the Lyapunov method, and the existence condition of the 1/3 subharmonic resonance of the quasi-zero-stiffness vibration isolation system is deduced. According to the approximate analytical solution, the primary resonance and subharmonic resonance force transmissibility of the quasi-zero-stiffness vibration isolation system with dry friction damper are obtained respectively. Compared with the numerical solution, the accuracy of the approximate analytical solutions of the primary resonance and subharmonic resonance of the quasi-zero-stiffness vibration isolation system is verified. By using the approximate analytical solution of the system, the effects of quasi-zero stiffness parameters and dry friction force on the amplitude-frequency response and force transfer characteristics for the primary resonance and subharmonic resonance of the system are analyzed in detail. The results show that the subharmonic resonance of the quasi-zero-stiffness vibration isolation system in the primary resonance region can be eliminated by selecting appropriate dry friction force parameter. The addition of dry friction damper can not only improve the amplitude suppression effect of the quasi-zero-stiffness vibration isolation system in the low frequency region, but also reduce the initial vibration isolation frequency. However, it will increase the force transmissibility of the system in the vibration isolation frequency band with vibration isolation effect.