Nonlinear output frequency response functions developed from the Volterra series is a new concept. Based on the concept, an explicit analytical relationship between the transmissibility of vibration isolator and the nonlinear characteristic parameters was derived for a wide class of nonlinear isolators that have nonlinear anti-symmetric damping characteristics.Further, the effect of the nonlinear damping parameters on the force and displacement transmissibility of vibration isolators was studied. The results show that, although the appearance of super-harmonic components for the nonlinear vibration isolators are subjected to the sinusoidal vibration excitation, the assessment of it’s transmissibility can be simply investigated from the relationship between the fundamental harmonic components of the input and outputs of the nonlinear isolators. Moreover, the introduction of a nonlinear anti-symmetric damping into vibration isolators can significantly suppress both the force transmissibility and the displacement transmissibility over the resonant frequency region, but has almost no effect on the transmissibility at non-resonant regions. These conclusions are helpful in the analysis and design of the nonlinear vibration isolators with nonlinear anti-symmetric damping.