The resonance of single-degree-of-freedom nonlinear impact oscillator to combined deterministic and random excitation is investigated. The method of harmonic balance, perturbation method and the method of stochastic averaging are used to determine the response of the system. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may change form a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state responses, one is a non-impact response, the other an impact response.