Traditional multi-layer anti-reflection films often encounter phase-matching issues in the infrared spectrum. Furthermore, they exhibit increased sensitivity to incident angles, particularly at large angles. While moth-eye structures can reduce angle dependency, achieving ultra-wide angle and broadband anti-reflection requires high aspect ratios, which present significant fabrication challenges. In this research, a hybrid anti-reflection micro-nanostructure is designed for broadband and ultra-wide angle applications, utilizing thin film interference theory and the effective medium approximation. Through comprehensive analysis of various parameters including periodicity, height, top diameter, and bottom diameter of the moth-eye structure, we have effectively attained a low aspect ratio of approximately 3.18. This achievement effectively addresses the challenges associated with fabricating high aspect ratio structures. Compared to traditional multilayer films, the hybrid micro-nanostructure presents a significant advantage by substantially reducing reflectivity over a wide spectrum (3-5 mu m) and at wide angles (0-60 degrees). The hybrid structure exhibits reflectivity below 6 % within the 60-75 degrees range, with an average of 6.9 % at an incidence angle of 80 degrees. Therefore, this hybrid structure can be widely applied in optical components such as infrared lenses, sensors, and windows. By efficiently reducing light reflection losses, it possesses the potential to augment the sensitivity and resolution of these optical elements.