The atomic diffusion in L1₀ ordered phase is investigated using on-the-fly kinetic Monte Carlo simulations. We construct a simple model system of L1₀ ordered phase. Although a simple model system is employed, the simulation results reveal quite complex aspects of the atomic diffusion. It is found that the activation energies of both constituent atoms change significantly depending on the composition and that the correlation factor makes the activation energy larger for both atoms. It is also demonstrated that the diffusion anisotropy in the L1₀ phase which is observed in the experiment is reproduced. We discuss the different diffusion behavior of the constituent atoms, and clarify the mechanism of the diffusion anisotropy in L1₀ phase.