A quasi-zero-stiffness vibration isolator with a variable load is designed to make up for the weakened ability to isolate vibration caused by the changed load. First, the principle of the vibration isolator is discussed in terms of its static characteristics based on its mathematical model. Then, the main resonance response is analyzed by the averaging method including the amplitude-frequency characteristic function of relative displacement and the displacement transfer rate of vibration. Besides, the rules of vibration changing with the parameters are investigated. The results show that the vibration isolator adapts to load by changing the angle of the quasi-zero-stiffness spring when the resonance is weakened and the initial isolation frequency is reduced with increasing angle. The vibration isolator is also characterized by gradual hardening, which compresses the resonant frequency bandwidth and reduces the descending frequency so that the quasi-zero-stiffness isolator with variable load excels the normal one in the low-frequency isolation performance.