The influence of a nonlinear damping which is a function of both the velocity and displacement is investigated for a single degree of freedom (sdof) isolator. The analytical relationships between the force or displacement transmissibility and the nonlinear damping coefficient are developed in the frequency domain for the isolator systems subjected to both force and base excitation. It is theoretically shown that the cubic order nonlinear damping can produce much better isolation performance, i.e., obvious peak suppression at resonant frequency and very close transmissibility to system linear dampingover non-resonant frequencies under both force and base displacement excitations. Moreover, when only the pure cubic order nonlinear damping is used without linear damping, the force or displacement transmissibility is even better. The results are compared with the other nonlinear damping terms previously studied in the literature. Numerical studies are presented to illustrate the results.