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 dependence of the skyrmion speed on edge thickness and width in the fluted nanostripe and explain theoretically with micromagnetics. It provides guidance for the design and development of spintronic devices based on nanostripes.