Grain growth is an important phenomenon in various thin films that comprise integrated circuits and magnetic disks. This paper demonstrates a three-dimensional Monte-Carlo (MC) simulation model to study grain growth in a binary Pt-Co system. In the formation of this system, a disordered phase is obtained, but later, it is transformed to an ordered phase through heat treatment. Using two methods, random nucleation and film growth, the grain growth of the single disordered phase was simulated. In simulating the order/disorder transition, the film-growth technique was employed, and the effect of surface energy, grain-boundary energy (GBE), and stability of the disordered and ordered phases was examined. The results show that the number and distribution of the nuclei of the ordered phase play an important role in grain size and grain morphology. It was also found that the formation of the columnar structure retarded grain growth and that the anisotropic GBE led to larger grain size.