According to the fact that it is difficult to satisfy the requirement of high structure stiffness and thermal stability with traditional support methods for large aperture rectangular reflector under self-gravity and large temperature changes, a spherical hinge support structure is introduced to effectively improve the surface accuracy of large aperture rectangular reflector under self-gravity and thermal load. Theoretical model analysis was conducted and analytic solutions were derived which could be useful to guide the optimization design of the support structure and predict the stiffness at the design phase. Finite Element Analysis is conducted for the spherical hinge bipod support of a 540×437 reflector. The result indicates that this kind of support structure can effectively improve the assembles’ thermal stability and stiffness and well satisfy the requirement.