Based our previous work [Mod.Phys.Lett.A 22 (2007) 783,Gen.Relat.Grav.39 (2007) 653],some properties of modified Chaplygin gas (MCG) as a dark energy model continue to be studied mainly in two aspects: one is the change rates of the energy density and energy transfer,and the other is the evolution of the growth index.It is pointed that the density of dark energy undergoes the change from decrease to increase no matter whether the interaction between dark energy and dark matter exists or not,but the corresponding transformation points are different from each other.Furthermore,it is stressed that the MCG model even supports the existence of interaction between dark energy and dark matter,and the energy of transfer flows from dark energy to dark matter.The evolution of the interaction term with an ansatz 3Hc2p is discussed with the MCG model.Moreover,the evolution of the growth index f in the MCG model without interaction is illustrated,from which we find that the evolutionary trajectory of f overlaps with that of the ACDM model when α> 0.7 and its theoretical value f≈0.566 given by us at z=0.15 is consistent with the observations.