To monitor and research 30.4 nm radiation generated by the plasmasphere, a lunar-based Extreme Ultraviolet(EUV) camera was developed.A multilayer mirror optical system and a 30.4 nm photon counting detector were adopted as the main body of the camera, and a two-dimensional tracing mechanism drived by a stepping motor was used to trace the earth. Aim to the vibration and impact from the process of satellite launching, orbit changes from earth′s to moon′s, moon landing, and the cruel temperature environment of the moon, the optical-mechanical design of EUV camera gave a consideration to the environmental adaptability. After the optimization by finite element analysis,it shows that the first order resonant frequency of the optical-mechanical structure is 49.3 Hz with the mass less than 15 kg, the motion mechanism operates freely within -50～+80 ℃, and the mirror surface accuracy (RMS) is 13.44 nm(<14 nm) under the load of uniform temperature drop of 50℃.Those results meet the technical requirements of the camera.