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The generalized cell mapping (GCM) method is used to obtain the stationary response of a single-degree-of-freedom.Vibro-impact system under a colored noise excitation.In order to show the advantage of the GCM method,the stochastic averaging method is also presented.Both of the two methods are tested through concrete examples and verified by the direct numerical simulation.It is shown that the GCM method can well predict the stationary response of this noise-perturbed system no matter whether the noise is wide-band or narrow-band,while the stochastic averaging method is valid only for the wide-band noise.