In this paper, we propose a new method to correct the perspective distortion that occurs in the process of acquiring the integral images. In the proposed method, the distortion correction is based on the spectral characteristics of integral images. As element images of an integral image are repeated nearly periodically, its Fourier spectrum is given as an impulse train. On the contrary, the impulse train do not appear in the spectra of distorted images. In the proposed method, therefore, the perspective distortion parameters are detected by using the characteristics of the spectrum obtained through the Fourier transform, and then the distorted images are corrected by using the parameters. Through experiments, we verify that the proposed method effectively works for the perspective distortion correction.