<p>The quasi-zero stiffness (QZS) isolator exhibits significantly better isolation capability than traditional isolators in the low-frequency range due to its lower natural frequency in the working range. Currently, most studies on the response of QZS vibration isolators are based on a single-periodic excitation, which does not simulate realistic and complex environments well. This paper focuses on the response of QZS system under quasi-periodic (QP) excitation, establishes a dynamics model under quasi-periodic excitation for a class of classical QZS vibration isolator configurations, obtains the response of the system under quasi-periodic excitation by using the MHBM method, analyzes the effects of different structural parameters and excitation parameters on the final response of the system, and investigates the distribution of the frequency components in the response and their influence on the frequency-response curves. On this basis, the bifurcation phenomenon and chaotic motion of the QZS system under QP excitation were discussed. The results show that QP excitation makes the nonlinear response of the QZS isolator more complicated and more sensitive to the changes in parameters, especially to the changes in the external excitation amplitude. It leads to the appearance of more unstable regions before the resonance peak of the system response, which may result in chaotic motion. QP excitation also increased the force transfer rate of QZS isolators before the resonance peak and reduced the isolation frequency band, resulting in a decrease in the isolation performance of QZS isolators.</p>