Steady state properties of a kinetic model of Smolen- Baxter- Byrne [P. Smolen, D. A. Baxter, J. H. Byrne, Amer. J. Physiol. Cell. Physiol. 274, 531 (1998)] are investigated in presence of two time- correlated noises. The steady state probability distribution can be obtained by solving the Fokker- Planck equation. It is found that both the correlated- time between the white noise and the colored noise and that between the colored noises can convert the bistability to monostability while the former activates the transcription and the latter suppresses it.