Molecular dynamics (MD) simulation is performed to study the diffusion and phase separation process in binary Lennard-Jones (LJ) liquid. It is found that the growth of phase separation with temperature can be divided into two stages. The first is the fast-growth at high temperatures and the second is the steady-growth at low temperatures. Diffusion activation energy in the phase separation system is not a constant, but a function of temperature and follows the relation of E=a+bTc. The influence of the sizes of the components on the phase separation is also discussed. The results shows that the diffusivity increases when the component size decreases. This facilitates the phase separation.