The invention discloses a three-cylinder type large-capacity magneto-rheological damper for vibration control of a large civil engineering structure, which comprises a magneto-rheological damping cylinder (9), a puddle damping cylinder (5), an auxiliary cylinder (19), a magneto-rheological main piston (23), a puddle piston (6), a piston rod (17), a sealing baffle (20), a damping channel (16), a cylinder cover (3) and a spherical hinge joint (13), wherein magneto-rheological liquid (11) is filled in the magneto-rheological damping cylinder, and an annular excitation coil (8) capable of generating a magnetic field is arranged in the magneto-rheological damping cylinder; and the puddle damping cylinder is arranged adjacent to the magneto-rheological damping cylinder, and elastic puddle (7) is filled in the inner cavity of the puddle damping cylinder, thus the damper can generate large damping under the condition of large displacement, and the safety of the damper can be improved. By arranging a displacement splitting mechanism (18), the magneto-rheological damper has high rigidity and large damping in a low-frequency region and has low rigidity and small damping in a high-frequency region. Compared with the traditional magneto-rheological damper with the same size, the maximum capacity of the damper of the invention is improved by more than one time, and the vibration control of the large civil engineering structure is more effective.