A design approach of the theoretical film system with broad-angle extreme ultraviolet (EUV) multilayers coatings based on the real-coded quantum evolutionary algorithm (RQEA) is proposed. Based on the RQEA and the real-coded genetic algorithm (RGA), the theoretical design and analysis for Mo/Si multilayers coatings with broad angles is performed. It is found that the RQEA has obvious advantages of small population, high efficiency, and high accuracy, which makes the RQEA possess potential application value in the field of optical film design. In addition, the broadband Mo/Si multilayer coatings with reflectivity of up to 50% at incidence angle of 0°-18° and at incident wavelength of 13.5 nm are designed.