Based on Fourier-Bessel transformation, diffraction field distribution of Gaussian beam limited by the circular grating is calculated and analyzed. Compared with plane wave,the results show that, if the circular grating radius is 1.5 times of the incident light spot radius, with number of rings increasing, the variation of FWHM decreasing first and then increasing, power ratio of the central spot decreasing, the intensity of central principal maximum decreasing,which are accordance with these of plane wave. But the variation of central spots radius and secondary maximum intensity are different with these of plane wave.If number of rings is less than 5, diffraction field distribution of Gaussian beam limited by the circular grating change irregular. If number of rings is more than 10,diffraction field distribution change unobvious. If number of rings tends to infinite,the central spots radius, FWHM and secondary maximum intensity tend to these of Gaussian beam diffraction limited by circular aperture, power ratio of the central spot is equal to 1/2 of that Gaussian beam diffraction limited by circular aperture, and central Maximum light intensity is equivalent to 1/4 of that of Gaussian beam diffraction limited by circular aperture.