In this paper, a graded SiNx and SiOxNy structure is proposed as antireflection coatings deposited on top of amorphous silicon (α-Si) thin-film solar cell. The structural parameters are optimized by differential evolution in order to enhance the optical absorption of solar cells to the greatest degree. The optimal design result demonstrates that the nonlinear profile of dielectric constant is superior to the linear profile, and discrete multilayer graded antireflection coatings can outperform near continuously graded antireflection coatings. What's more, the electric field intensity distributions clearly demonstrate the proposed graded SiNx and SiOxNy structure can remarkably increase the magnitude of electric field of a-Si:H layer and hence, enhance the light trapping of a-Si:H thin-film solar cells in the whole visible and near-infrared spectrum. Finally, we have compared the optical absorption enhancements of proposed graded SiNx and SiOxNy structure with nanoparticles structure, and demonstrated that it can result in higher enhancements compared to the dielectric SiC and TiO2 nanoparticles. We have shown that the optimal graded SiNx and SiOxNy structure optimized by differential evolution can reach 33.31% enhancement which has exceeded the ideal limit of 32% of nanoparticles structure including plasmonic Ag nanoparticles, dielectric SiC and TiO2 nanoparticles.