The invention provides a flexible back supporting device for a large-caliber reflector. The supporting device comprises the large-caliber reflector, a lens back plate, a supporting plate, a joint plate, a screw, flexible branch hinges, sliding flexible hinge supports, a flexible hinge connecting rod and a driving system. The three flexible branch hinges and the joint plate together form a combined hinge to constrain three degrees of horizontal moving freedom of the large-caliber reflector, the pitching and deflecting movements of the large-caliber reflector are achieved through flexible hinge blocks of the sliding flexible hinge supports and the driving system, when the driving system is tightly locked, the two degrees of rotating freedom of the large-caliber reflector are constrained, and the degree of the plane inner rotating freedom of the large-caliber reflector is constrained through the flexible hinge connecting rod. The flexible hinge structure is adopted as the supporting and positioning mechanism of the large-caliber reflector, nanoscale positioning precision is achieved, and the structural stability and the precision stability are ensured through matched design of the flexibility and the moving precision of the large-caliber reflector. The flexible back supporting device has the advantages of being simple in structure, stable in movement, free of friction or gaps, needless for lubrication and high in moving sensitivity.