In this paper, the stationary responses of a single?degree?of?freedom inelastic vibro?impact system with two?sided asymmetric barrier in the presence of wide?band noise are studied. The generalized Hertz contact model is applied to simplify the impact restoring force of the vibro?impact system. The averaged Ito stochastic differential equation of the system under wide?band random excitation was obtained through the stochastic averaging method, based on the generalized harmonic functions. After solving the stationary FPK equation corresponding to the stochastic differential equation, the stationary probability densities of amplitude, total energy, displacement and the joint probability density of velocity, and displacement of the system are gained immediately. In addition, the stochastic responses of the system are approximated as Markov processes, and the generalized cell mapping method is applied to derive the approximate stationary responses. It demonstrates that the results obtained by the stochastic averaging method and the generalized cell mapping method are in a great agreement with those from Monte Carlo simulation.