The lattice Boltzmann method is used to simulate numerically the droplet motion driven by Marangoni effect, which is induced by surface tension gradient on the solid-liquid interface, with the consideration of interaction between solid and liquid molecules. The computation results are well compared with the theoretical prediction available for smaller surface tension gradient, whereas the translation velocity of droplet is smaller than the theoretical value for larger gradient, because some assumptions, such as the quasi-equilibrium and non-deformable droplet, are not satisfied in the theoretical analysis anymore. Vortical structure with a solid-like core is found in the droplet when it moves to the hydrophilic end. The variations of velocity and contact angle of droplet are found to be oscillating with time for larger gradient of wettability.