Magnetic skyrmion can be used as information carrier of logic devices because of its nano size and topological properties. Here, we introduce a wedge-shaped circular track structure, in which the cycle motion of skyrmion in the ferromagnetic track is induced by the gradient of voltage-controlled magnetic anisotropy. Compared with the straight track, the process of generation and annihilation of skyrmion is avoided due to the recycling of skyrmion. Furthermore, the logic of the JK flip–flops is successfully implemented in the wedge-shaped circular track, which provides guidance for the design of skyrmion-based sequential logic devices.