Based on the model describing the regulation of the PRM operator region of λ phage proposed by Hasty et al.[Proc. Nat. Acad. Sci. 97(2000)2075], we study the steady-state probability distribution properties of the model in the presence of correlated Gaussian white noise. We find that the degree of correlation of the noises can affect the form of the steady-state probability distribution. When the degree of correlation of the noises increases, the form of the steady-state probability distribution changes from a bimodal into a unimodal structure.The steady-state probability distribution extrema have also been investigated. We find that noise correlation can change the positions of the extreme value of the steady-state probability distribution of the model greatly.