Based on a genetic bistable switch model coupled with a gene oscillator model, we have constructed a mesoscopic stochastic model for the coupled synthetic gene network, and studied how internal noise would influence the oscillation of such a system. We found that the state-to-state transitions can occur if the internal noise is taken into account, and the performance of resulting oscillation can reach a maximum in a certain internal noise level, which indicates the occurrence of internal noise stochastic resonance (SR) and makes the coupled gene network work as a stochastic resonator. The potential role of such an effect on gene expression systems is also discussed.