Color non-uniformities caused by a dispersion effect can seriously affect the image quality for a diffractive waveguide display system. In this work, we propose a subwavelength multilayered dielectric grating structure by a rigorous coupled wave analysis as a novel coupling grating, to the best of our knowledge, for waveguide-based near-eye displays to overcome the "rainbow" effect. Such a grating structure exhibits a tunable high-efficiency resonance in first-order diffraction due to resonant coupling of incident light with the grating structure. A further analysis of the resonant behaviors helps us get a clear understanding of the underlying physics for the mode excitation and resonant coupling process. The first-order resonance with a diffraction efficiency of more than 60% can be achieved with the resonant angle continuously shifted to get a large field of view. The resonant angle, diffraction efficiency, and spectral linewidth can be easily tuned by the geometrical parameters of the grating structure.