A bionic moth-eye sub-wavelength periodic micro-nanostructure of ZnS MS material, with broadband and wide-angle antireflection properties is designed by the rigorous coupled-wave analysis method. According to the rigorous coupled wave theory, a suitable control of periodic size, smaller than the ratio between the incident wavelength and the refractive index of materials, makes the high-order diffracted wave as an evanescent wave, and thus the broadband antireflection efficiency of this moth-eye structure is enhanced. The finite difference time domain algorithm is used to investigate the effects of moth-eye structural period, bottom diameter, structural height and top diameter on spectral transmissivity. Moreover, four structural parameters are optimized. In addition, three characteristic wavelengths in the visible, near-infrared and middle-infrared regime are selected for the electric field analysis under a wide-angle incidence. The research results show that in the short-wavelength range, the moth-eye wide-angle anti-reflection performance is determined by the anti-reflection and forward-scattering ability of this structural surface, while in the long-wavelength range, the moth-eye structure is regarded as a ZnS MS plane film, and its spectral properties are mainly affected by the Fabry-Perot interference. This study provides a theoretical basis and a design method for the design of moth-eye wide-angle structures under different wavelengths.