A typical quasi-zero stiffness (QZS) vibration isolator composed of two lateral springs and a vertical spring has been widely studied previously, aiming to widen the frequency range of isolation without increasing the static displacement. However, there is still a gap between the previous dynamic model and the practical application, due to the neglection of some factors that may exist in practical situations. In this paper, a more accurate dynamic model is established with consideration of these practical factors. The dynamic behavior and dynamic characteristics of this typical QZS isolator are analyzed based upon the accurate dynamic model. The biggest difference between the newly proposed dynamic model and the previous one lies in the damping characteristics. Therefore, we specially investigate the damping effects, from which it is found that the vibration isolation performance can be further enhanced by proper design of the damping parameters.