The invention relates to a large-tonnage elasticity-damping composite damping device. The large-tonnage elasticity-damping composite damping device comprises a damping cylinder, an outer cylinder sleeve, a piston rod, a left spherical hinge base, a right spherical hinge base and a lengthening sleeve. The right end of the damping cylinder is connected with the right spherical hinge base through the lengthening sleeve, and the left end of the damping cylinder is arranged in the outer cylinder sleeve. The outer cylinder sleeve is arranged outside the damping cylinder and the lengthening sleeve in a sleeving manner. The left end of the outer cylinder sleeve is fixedly connected with the left spherical hinge base, and the right end of the outer cylinder sleeve is in sliding connection with the outer side of the lengthening sleeve. A damping cavity filled with a damping medium is arranged in an inner cavity of the damping cylinder. The piston rod penetrates the damping cavity and is connected with the left spherical hinge base. A spring cavity is formed by the damping cylinder, the outer side of the lengthening sleeve and the inner side of the outer cylinder sleeve. Resistance blocks are arranged at the two ends of the spring cavity. A spring device is arranged in the spring cavity. The spring device is in a compressed state and abuts against the resistance blocks at the two ends. Compared with the prior art, damping and springs are connected in parallel, the self-reset function is achieved, and the large-tonnage elasticity-damping composite damping device can be suitable for damping of large-span suspension bridges and cable-stayed bridges and displacement control of girders.