Recent 3-Dimensional Atom Probe (3DAP) experimental observations showed the formation of spherical γ-precipitates at a central region of γ’ phases in nickel based superalloys. The γ precipitates should give a significant effect to the material strength. Whereat, in this work, we first developed a simulation technique for the investigation of the formation of γ-precipitates in γ’ phases, which is based on a combination of an Embedded Atom Method (EAM) interatomic potential designed for Molecular Dynamics (MD) and the kinetic lattice Monte Carlo (KLMC) method. As a demonstration of the KLMC simulation, the formation of the L12 structure was simulated from an initial state with randomly distributed aluminum atoms (25at.%Al). Finally, the γ’ phase with the L12 structure is formed in the entire simulation volume. To understand the fundamental mechanism of the formation of the L12 structures, the binding energies between a pair of aluminum atoms in a nickel single crystal were calculated using MD method. The result gave a clear picture of the mechanism. The stability of the γ-precipitate was also investigated using the MD method. Finally, the formation of γ-precipitates was simulated using the KLMC method. The dependence of the formation on the temperature condition is discussed.