The effects of void-based photonic crystal mirrors on reflectivity and dissipation for extreme-ultraviolet (EUV) radiation at near-normal illumination are studied. The mirrors are based on a multilayer coating comprising alternating layers of molybdenum (Mo) and silicon (Si) with 40 periods. By embedding voids in silicon films instead of molybdenum films, we found that the reflectivities of the mirror are increased and the absorptions of the mirror are decreased with the increments of the voids. On the other hand, the reflectivities of the mirror are decreased and the absorptions are increased by embedding voids in the molybdenum films, with the increments of the voids. Compared to the standard designs of 40 Mo/Si multilayer mirrors, which are currently used in most EUV or soft x-ray applications, the reflectivity of the void-based photonic crystal mirror in our study can reach from 73.43 to 83.24% and the absorption can decline from 26.18 to 16.80%. In consideration of EUV bandwidth, the effects of illumination angles in the six-mirror projection system, the intermixing layers, and the variation of the coated absorber thickness on the reflection properties are studied. The proposed concept can be used in next-generation EUV lithography and soft x-ray optical systems.