The kinetics of spinodal decomposition of binary alloys in case of finite grain size and slow grain growth is studied by applying the Monte-Carlo method where a coupled algorithm of the spin-exchange Ising model and Q-state Potts model operates. The anisotropic energy of grain boundaries is incorporated by imposing a Potts spin lattice on the Ising crystal. We simulate the phase separation where the grain size is comparable with the spinodal length on the order of magnitude. It is revealed that the grain boundaries of low excess energy as rapid channel enhance the solute diffusion, whereas those boundaries of high excess energy hinder the solute diffusion. Depending on the system supersaturation, phase aggregation preferred at the grain boundaries is demonstrated. The spinodal kinetics is modulated by the grain growth so that the Lifshitz-Slyozov-Wagner law may no longer be applicable in spite of the scaling law roughly holds in present system.