To reduce the surface deformation of a star tracker reflector in a complex and execrable environment, a micro stress flexible support structure was designed according to the circular optical reflector subassembly. By defining the thickness, width and radius as design variables, the flexible hinge in an circular reflector subassembly was optimized. Then, the surface figure precision, structural strength and dynamic stiffness of the reflector subassembly in the thermal-structural coupling state were analyzed with the finite element method. Simulation results show that the natural frequency of the reflector is enough, which has a sufficiently high dynamic stiffness. Both surface precision RMS of the reflector (8.34nm, 9.26nm) have reached the index requirements of the optical system (λ/10, λ=632.8nm) under gravity and uniform temperature change from -20℃ to 65℃. The results show that the design for the micro stress flexible support structure is reasonable and feasible, and achieves the design goal.