A surface wettability gradient can break the equilibrium status of a liquid droplet and drives its unidirectional movement on the surface. We propose a conceptual design of the driving water droplet on a graphene surface and demonstrate that both speed and direction of the movement can be controlled via a continuous gradient of surface wettability using comprehensive molecular dynamics (MD) simulations. Controlling the water droplet toward linear and nonlinear arc paths is exemplified in one- and two-dimensional gradients of surface wettability, respectively. Unbalanced Young's equation is extended to understand the speed of the droplet movement, and the predications agree well with MD simulations.