Adopting the linear approximation method, a loss model for a single-mode laser driven by pump noise and quantum noise whose real and imaginary parts are correlated is studied. We investigated the intensity correlation function, which describes the dynamic property of a laser and varies with time. Moreover, the valid range for the linear approximation method is obtained, and the effects of the intensities of the pump noise and quantum noise on the variance of the laser intensity, and the correlation coefficient between the real and imaginary parts of the quantum noise, are discussed in detail. We find that the valid range is extended in the case of small quantum noise and far form threshold, and it is the largest in the case of small quantum noise, far form threshold and no correlation between the real and imaginary parts of the quantum noise.