The invention discloses a cable towing chain movement device for curved power supply and a working method of the cable towing chain movement device. The cable towing chain movement device comprises a towing chain arranged in a guide groove sideways, wherein the shape of the guide groove is determined by a running trajectory curve of the movement device; one end of the towing chain is connected with a power source bracket, and the other end of the towing chain is fixed on a connecting frame of the movement device; a moving frame is connected with a moving frame driving device; an arc groove for supporting the towing chain is machined in the moving frame. The cable towing chain movement device and the working method thereof have the benefits that rollers are arranged on the three surfaces, in contact with the guide groove, of the towing chain, and can roll on the guide groove and the moving frame, so that the phenomenon of excessive abrasion of the towing chain is avoided; the device can be applied to places where the towing chain is required to run along a curve, and is particularly applicable to places with limitations to electric sparks.