For the diffractive optical element (DOE) realizing beam shaping in the fractional Fourier transform domain,the transform matrix calculated by the discrete sampling points was compared with that calculated by the Fresnel integral,and the discretization error of the intensity distribution on the output plane was qualitatively obtained.Simulated results show this discretization error cannot be neglected.Therefore the Fresnel integral should be used to obtain the true intensity distribution on the output plane.Because the transform matrix calculated with the Fresnel integral was non-unitary,YG algorithm was used to design the DOE realizing beam shaping in the fractional Fourier transform domain in this paper.