As an optical element, diffraction grating is of considerable importance in many research fields. In this paper, Fourier analysis method is used to analyze the Fraunhofer diffraction phenomena of plane and convex holographic gratings under various conditions. Based on the transmittance function, the law of complex amplitude distribution, intensity distribution and spectral distribution on the diffraction screen is derived. For the planar and convex holographic gratings in the spectrometer design, the inherent laws of optical phenomena can be understood more deeply. In particular, the convex holographic gratings are analyzed as a combination of amplitude type plane grating and phase type spherical mirror, rather than being considered separately in most literature.