The invention relates to a three-cutting torch curve groove cutting device. The cutting device comprises a connection frame, a servo rotary motor and a rotary main shaft which is positioned above the connection frame, wherein a rack bar is arranged on the connection frame; a central cutting torch connection frame is fixedly arranged on the rack bar; two sides of the central cutting torch connection frame are provided with left and right moving bodies; the left moving body is connected with a left hand wheel which is meshed with the rack bar; the right moving body is connected with a right hand wheel which is meshed with the rack bar; a left cutting torch holder is arranged on the left moving body; a right cutting torch holder is arranged on the right moving body; an output shaft of the servo rotary motor is connected with an input shaft of a reduction gearbox; output gears are arranged on the output shaft of the reduction gearbox; rotary gears are arranged on the rotary main shaft; the rotary gears are meshed with the output gears; and the lower end of the rotary main shaft is fixedly connected with the connection frame. The whole cutting device has a compact structure and is easy and convenient to operate. When a cutting program of a corresponding straight line or curve is input, the device can automatically complete the whole cutting working according to the requirements of a groove of the straight line or the curve.