Based on the Fresnel diffraction integral and Laguerre-Gaussian beam field distribution, the circular aperture diffraction, single slit diffraction and square hole diffraction of Laguerre-Gaussian beam are studied, and the effect of spiral phase structure on the field distribution of the diffracted light beam is analyzed as well. The degree of dispersion of the orbital angular momentum is also calculated using the well-known spiral spectrum, when Laguerre-Gaussian beam passes through a single slit or a square hole in the same case of Laguerre-Gaussian beam phase singularity locating at the center of a diffraction hole. According to the theoretical calculation results, it′s demonstrated that the orbital angular momentum does not disperse when Laguerre-Gaussian beam passes through a circular aperture.