A guided-mode resonant filter (GMRF) based on the structure of anti-reflection (AR) thin film waveguide is proposed to realize three-primary-color filter with narrow-band. The proposed grating consists of three parts: a sub-wave grating, a waveguide and a substrate. The effects of sub-wave grating and thickness of waveguide on the GMRF reflection spectrum are investigated in detail with the method of rigorous coupled-wave analysis (RCWA). Simulation results show that the structure of λ/4-λ/2-λ/4 can improve the performance of GRMF effectively. When the grating layer is located near the substrate, the cut-off band of the optimized filter for red, green and blue primary colors are 447, 349 and 279 nm, respectively. The reflectance is above 95% and reflection bands are all narrower than 0.2 nm. The optimized GMRF shows excellent performance with narrow band and can be useful for color synthesis and modulation.