A disc rubber vibration isolator with quasi-zero stiffness (QZS) was designed, and the characteristics of vibration isolation were studied. The QZS isolator was devised by assembling a reinforced disc rubber with negative stiffness in parallel with a vertical rubber cylinder with positive stiffness. By using Finite Element Analysis (FEA), the geometrical parameters of the reinforced disc rubber and the vertical rubber cylinder were achieved to ensure that the isolator's stiffness is close to zero at the static equilibrium position. And then, the characteristics of restoring force were analyzed, and the expression of restoring force was given as a polynomial only having cubic item by fitting the FEA simulations data. Moreover, the equation of motion of the vibration isolation system was obtained, and the isolation performance was evaluated theoretically based on Harmonic Balanced method, which was compared with that by using dynamic FEA. The results have shown that the QZS isolator significantly outperforms the corresponding linear one.