A work-implement external-shape measurement system including a measurement controller that measures an external shape of a work implement provided to a work machine , the work-implement external-shape measurement system comprising: an image-capturing device that captures an image of a side surface of the work implement , characterized in that the measurement controller is configured to extract a contour line of the work implement on the image of the side surface of the work implement , the image being captured by the image-capturing device , compute a position of a plane (S1) representing the side surface of the work implement in an image-capturing-device coordinate system (Co1) that is a three-dimensional coordinate system set for the image-capturing device , the position being computed on a basis of the image, and an internal parameter of the image-capturing device , on a basis of information on a position of any pixel on the contour line of the work implement on the image and the position of the plane (S1), compute a coordinate value of a point on the contour line of the work implement in the image-capturing-device coordinate system (Co1), the point corresponding to the any pixel, and convert the coordinate value of the point on the contour line of the work implement in the image-capturing-device coordinate system (Co1), the point corresponding to the pixel, to a coordinate value in a work-implement coordinate system (Co3) that is a two-dimensional coordinate system set for the work implement , and output the coordinate value of the point on the contour line of the work implement in the work-implement coordinate system (Co3) to a work-machine controller of the work machine . an image-capturing device that captures an image of a side surface of the work implement , characterized in that the measurement controller is configured to extract a contour line of the work implement on the image of the side surface of the work implement , the image being captured by the image-capturing device , compute a position of a plane (S1) representing the side surface of the work implement in an image-capturing-device coordinate system (Co1) that is a three-dimensional coordinate system set for the image-capturing device , the position being computed on a basis of the image, and an internal parameter of the image-capturing device , on a basis of information on a position of any pixel on the contour line of the work implement on the image and the position of the plane (S1), compute a coordinate value of a point on the contour line of the work implement in the image-capturing-device coordinate system (Co1), the point corresponding to the any pixel, and convert the coordinate value of the point on the contour line of the work implement in the image-capturing-device coordinate system (Co1), the point corresponding to the pixel, to a coordinate value in a work-implement coordinate system (Co3) that is a two-dimensional coordinate system set for the work implement , and output the coordinate value of the point on the contour line of the work implement in the work-implement coordinate system (Co3) to a work-machine controller of the work machine . compute a coordinate value of a point on the contour line of the work implement in the image-capturing-device coordinate system (Co1), the point corresponding to the any pixel, and convert the coordinate value of the point on the contour line of the work implement in the image-capturing-device coordinate system (Co1), the point corresponding to the pixel, to a coordinate value in a work-implement coordinate system (Co3) that is a two-dimensional coordinate system set for the work implement , and output the coordinate value of the point on the contour line of the work implement in the work-implement coordinate system (Co3) to a work-machine controller of the work machine . <EOS>