Abstract: The approach of inferring the grating profile from its reflection spectrum is referred to as fiber Bragg grating (FBG) synthesis algorithm. Synthesis of FBG is of great significance for the design of special FBG to have desired characteristics. A simple and efficient method based on the coupled-mode theory and transfer matrix method for the design of complex FBG was proposed. The method takes into account only the first reflection, exploiting the approximate Fourier transform relation that exists between the filter spectral response and the coupling function. Its low algorithmic complexity enables the fast synthesis of weak reflection FBG. The method is illustrated by designing two types of dispersion compensators for the applications of optical fiber communication systems, constant dispersion coefficient with 17ps/nm in its 3dB passband and linear dispersion slope coefficient compensators. Numerical simulation results show that the method is very effective for parameter reconstruction of fiber gratings according to desired reflectivity characteristics and can be applied in the design of complex filter based on the reflectivity characteristics of fiber gratings.