Aiming at the problem of support structure for K mirror in Alt- az telescope, the union support structure which includes three- point bottom support and side support is designed, and the experimental study about support structure is completed. According to the relation of radius-thickness ratio and shape change, the thickness of mirror is determined. Based on kinematics mount principle of mirror, the bottom and side support structure is designed, and the structure includes flexibility hinge which ensure that the support stress is not interference. Then, the parameter model of K mirror is established by Ansys software, the points of support position are optimized, and root mean square (RMS) of mirror surface diguer is obtained. Finally, the splice experiment is promoted, and platform of detection experiment is constructed. Experimental results indicate that the RMS of mirror is 12 nm, the peak valley (PV) of mirror is 76 nm, the experimental results are close to the simulation results. It can certify that the support structure of K mirror is validity and feasibility, and it accords with the design requirements of K mirror system.