Taking a SiC mirror with an aperture of 500mm for example, the supporting characteristic of rear support in centre was studied based on spercific lightweight shape and supporting structure by using finite element analysis, and the effects of structural parameters on the performance were analyzed. The analyses point out that the optimal proportion of the diameter of support hole to the aperture of mirror is 0.23, the optimal rear shape of mirror with different aperture should be determined by using optimization method, and the surface accuracy can be improved by increasing the support depth when the gravity in radial direction. The analyses of supporting structure indicate that the radius of bolt circle at the bottom of the flexible connector is the key factor which has great influence on both the surface accuracy under the load case of temperature variation and the first order frequency of mirror subassembly, so it is considerable to weigh the requirment of surface accuracy and structural basic frequency when chosing the optimal value of the radius. The surface accuracy of the mirror supported by rear in centre is less affected by the assembling stress from outside and not sensitive to notch depth changing. The support length has a great influence on dynamic stiffness of the structure and its decrease will increase the first order frequency of mirror subassembly. Finally the maximum aperture of the space SiC mirror supported by rear in centre is intended to be 750 mm, which means that the mirror supported by rear in centre without of structural constraint can be satisfied with the refered requirment when its aperture is less than 750 mm.