The effect of the aperture-averaging is studied for the case of a finite detector aperture when the receiver detects the light intensity of which the complex field amplitude is an elliptical Gaussian probability-density function, and a more general aperture-averaging function is obtained. The aperture-averaging intensity fluctuation statistical distribution is analyzed theoretically for the case of a finite detector aperture. The results show that the scintillation probability follows the logarithmic normal distribution when the correlation speckle number is large in the receiver aperture. The conclusion agrees with the previous experimental measurements.