Many investigations show that the grain boundary can significantly affect the pattern formation and kinetics of spinodal decomposition, however, these works rarely consider the effects of the kinetic properties of grain boundaries. In this work, the spinodal decomposition process near moving grain boundaries was investigated by the phase-field model. The simulation results indicate that the grain boundary-directed spinodal pattern is anisotropic, and with the increase of atom mobility inside the grain boundary, the pattern of the decomposed phase changes from parallel to the original grain boundary to perpendicularity. Moreover, the spinodal decomposition also affects the migration process of the grain boundary in turn.