Recently, the gyrator transform (GT), which is also a kind of linear canonical transform (LCT), has been researched in the fields of image processing, mathematics and optics; the calculation of discrete GT can be implemented by Fresnel diffraction integral in free space under paraxial approximation; in this paper The expression of gyrator transform (GT) is rewritten by using convolution operation, from which GT can be composed of phase-only filtering, Fourier transform and inverse Fourier transform. We investigate an algorithm computing discrete GT by simulating the convolution expression of fractional Fourier transform. Some simulations in order to evaluate the difference between inverse transformed image and original image are presented to demonstrate the validity of the algorithm, the reversibility of numerical algorithm of transform is important to the field of optical information processing, such as image encryption, filtering and correlation.