The invention relates to a polishing tool, in particular to a metal curved surface flexible polishing tool. The metal curved surface flexible polishing tool comprises a polishing head, an outer shell, a front end cover, a rear end cover, a gasket, a thrust bearing, a universal joint, a gear transmission mechanism, a coupler, a motor and a flange, wherein the polishing head is provided with three round polishing heads which are evenly distributed on a circumference, the center connecting lines of the three round polishing heads form an equilateral triangle, the gasket is located at the bottom of the polishing head, the thrust bearing is located between the polishing head and the gasket, the thrust bearing and the gasket are fixed together, a spring is located at the bottom of the gasket, the two ends of the spring are fixed on the gasket and the front end cover, a shaft of the polishing head is connected with a gear shaft of the gear transmission mechanism through the universal joint, and a driving gear shaft of the gear transmission mechanism is connected with a power output shaft of the motor through the coupler. The gear transmission mechanism, the coupler and the motor are packaged inside a shell body formed by the outer shell, the front end cover and the rear end cover, heat radiation holes are formed in the outer shell, and the flange is externally connected with an industrial robot.