Current-induced skyrmion motion is studied with theory and simulation of micromagnetism. Compared with those in the nanostripe, the maximum driving current density (J_(max)) and the maximum skyrmion speed (V_(max)) increase significantly in a fluted nanostripe structure which provides greater skyrmion-edge repulsion force to suppress transverse displacement of the skyrmion. As the driving current density increases, the skyrmion speed increases to V_(max), and then decreases or remains unchanged. As increasing the edge width or thickness, J_(max) and V_(max) increase linearly. We show dependenc...