The invention discloses a numerical-control flexible roll bending machine for three-dimensional variable-curvature sheet metal parts. The numerical-control flexible roll bending machine comprises a base, a left machine frame, a right machine frame, a turnover device, a rigid roller, a flexible roller coated with polyurethane rubber, two side rollers, an upper roller supporting device, a side roller supporting device, a driving device, a lifting device and a dedicated numerical control system. The rigid roller, the flexible roller and the two side rollers are installed on the left machine frameand the right machine frame. According to the numerical-control flexible roll bending machine, the flexible roller is located under the rigid roller and connected with the lifting device, a rigid upper roller is connected with the driving device, the lifting device drives the flexible roller to ascend and descend, the driving device drives the rigid upper roller to rotate, the upper roller supporting device and the lower roller supporting device conduct reverse supporting on the rigid upper roller and two lower rollers, and the phenomenon that in the plate rolling process, all rollers are subjected to flexural deflection due to reactive force is eliminated; and by controlling the depth, pressed into the flexible roller, of the rigid upper roller and the feeding positions of the two side rollers, the parts subjected to double variable curvature roll bending are obtained.