The misalignment error of the spliced diffraction telescope has an important influence on the imaging quality of the optical system. Therefore, the tolerance of the misalignment error of the spliced Fresnel lens is analyzed, and the theoretical calculation formula of the misalignment error based on Rayleigh criterion is derived. The tolerance of the optical system including the spliced primary mirror and achromatic optical path with an aperture of 1.5 m is analyzed. The simulation results show that the wavefront aberrations within the tolerance range meet the Rayleigh criterion and Streyer ratio, so the tolerance analysis can provide effective theoretical guidance for the installation, adjustment and detection of diffraction telescopes.