This　paper　considers　the　adaptive　synchronization　of　general　complex　dynamic　networks　via　state　predictor　based　on　the　fixed　topology　for　nonlinear　dynamical　systems.　Using　Lyapunov　stability　properties,　it　is　proved　that　the　complex　dynamical　networks　with　state　predictor　are　asymptotically　stable.　Moreover,　it　is　also　shown　that　the　rate　of　convergence　of　complex　dynamical　networks　with　state　predictor　is　faster　than　the　complex　dynamical　networks　without　state　predictor.