Based on the Fresnel diffraction integral, the diffraction pattern of a Laguerre-Gaussian beam passing through a single-slit has been studied. It is found that the diffraction fringes of the Laguerre-Gaussian beam will dislocate and bend which have also been demonstrated by experiments. The spiral spectra of the Laguerre-Gaussian beam passing through the single-slit are also investigated. It is shown that the spiral spectra will broaden with the existence of the single-slit. In addition, the phase distribution of the Laguerre-Gaussian beam in the diffraction plane has also been investigated. The research results can be used to measure the topological charges of vortex beams.