Laguerre-Gaussian (LG) beams attratts much attention in the fields of rotating micro-particle manipulation and information processing due to their special phase structures and related orbital angular momentum. In this paper the generation of LG beam by an amplitude grating was theoretically studied and the LG beams with azimuthal number of ±1 were obtained by the amplitude grating produced by the computer-generated hologram (CGH). Influences of main factors on the beam transformation were discussed.