1. An inspection method for a mouth section of a bottle-can, with respect to the bottle-can having the cylindrical mouth section in which a curl portion is formed by curling an open end thereof for a cap with a liner to be put on, by taking an image of an imaging area which is set to include a part of the curl portion for detecting asperity at the curl portion while rotating the bottle-can around a can-axis, the inspection method comprising steps of: a first-inspection process for eliminating the bottle-can in which existence of a low-brightness area is detected from a monochrome inspection-image which is obtained by imaging the curl portion with irradiating white light to the curl portion in an imaging area of the bottle-can which is conveyed along a main-conveyance path continuously and sequentially; and a second-inspection process for judging quality of the bottle-can while conveying the bottle-can which is eliminated by the first-inspection process along a secondary-conveyance path deviated from the main-conveyance path, by irradiating illumination lights having two colors from different directions to the curl portion in the imaging area along substantially a tangential direction of a cylindrical surface of the mouth section so as to image a color inspection-image, and distinguishing existence or not of the asperity on the curl portion from signal strengths of the light colors of the color inspection-image.