This paper studies the effects of cross-correlations between the real and imaginary parts of quantum noise on the laser intensity in a saturation laser model. It derives the analytic expressions of the intensity correlation function C(τ) and the associated relaxation time T(C) in the case of a stable locked phase resulting from the cross-correlation λq between the real and imaginary parts of quantum noise. Based on numerical computations it finds that the presence of cross correlations between the real and imaginary parts of quantum noise slow down the decay of intensity fluctuation, i.e., it causes the increase of intensity fluctuation.