With the linear approximation method, the intensity correlation function C(t) and normalized mean intensity fluctuation C(0) are calculated, which reflects dynamic properties of the laser. The time evolution of C(t) is discussed in a loss-noise model of single mode laser system by pump noise and quantum noise with cross-correlation real and imaginary parts. The influences on the time evolution of C(t) are analyzed from cross-correlation coefficient between the real and imaginary of quantum noise λq, intensities of the pump noise P and quantum noise Q, respectively. The time evolution of C(t) is a monotonous descending process, while the whole C(t) versus t curve falls down with noises intensity reducing and the cross-correlation between real and imaginary parts of the quantum noise weakening, which shows that the great influence of the noises intensity and the cross-correlation between real and imaginary parts of the quantum noise on the time evolution of C(t). When t increases, an extremum or three extrema appears in the C(t) versus λq curve. Finally, the valid range for the linear approximation method is discussed.