Quasi-zero-stiffness (QZS) vibration isolation system is designed to realize low-frequency and ultra-low-frequency vibration. Since the nonlinearity exists in the QZS system, various nonlinear dynamic behaviors inevitably influence the vibration isolation performance. Thus, the damping become the key to suppress the nonlinear effect. In this paper, the dynamic behavior of QZS system with three types of damping, viscous damping, hysteretic damping and nonlinear hysteretic, is discussed. The Duffing-Ueda equation is used to describe the dynamic motion of the QZS system, which is solved by the harmonic balance method (HBM). Considering the actual isolation application, the analysis is based on the displacement transmissibility. The analytical results are verified by the numerical results. The results reveal the three types QZS system provide different isolation effect under the same vibration environment. Thus, in actual engineering application, the type of damping should be chosen carefully.