  In this paper, we prove that K\"ahler-Ricci flow converges to a
K\"ahler-Einstein metric (or a K\"ahler-Ricci soliton) in the sense of
Cheeger-Gromov as long as an initial K\"ahler metric is very closed to $g_{KE}$
(or $g_{KS}$) if a compact K\"ahler manifold with $c_1(M)>0$ admits a K\"ahler
Einstein metric $g_{KE}$ (or a K\"ahler-Ricci soliton $g_{KS}$). The result
improves Main Theorem in [TZ3] in the sense of stability of K\"ahler-Ricci
flow.
