Despite the inefficiencies associated with current-induced spin torques, they remain the predominant mode of skyrmion propulsion. In this work, we demonstrate numerically that skyrmions can be transported much more efficiently with a voltage-controlled magnetic anisotropy (VCMA) gradient. An analytical model was developed to understand the underlying skyrmion dynamics on a track under the VCMA conditions. Our calculations reveal that the repulsive skyrmion-edge interaction not only prevents the skyrmion from annihilating but also generates most of the skyrmion propulsion. A multiplexed array of gate electrodes can be used to create discrete anisotropy gradients over a long distance, leading to the formation of a series of translatable skyrmion potential wells. Due to the strong confining potentials, skyrmions are transported at a 70% higher packing density. Finally, we demonstrated that this form of skyrmion propulsion can also be implemented on almost any 2D geometry, providing improved versatility over current-induced methods.