Stochastic resonance is a nonlinear cooperative effect between external signal and noise, in which the noise can play a constructive role to increase the signal-to-noise ratio in the detection of a weak signal. A surface catalytic reaction model, to describe oxidization of carbon monoxide carrying out far from equilibrium, was adopted to study the stochastic resonance. By computer simulation, we found noise can induce state-to-state transitions, and stochastic resonance behavior may appear at narrow bistable states or near discontinuous Hopf bifurcations, while a weak periodic signal riding on noise is input controlling.