A dynamic renormalization-group method is generalized to explore the anomalously dynamic scaling property of kinetic roughening growth equation and the general conclusion on the anomalous exponents of the growth equation with spatially and temporally correlated noise is drawn. The results of the anomalous exponents are employed in several typical local growth equations，which include the Kardar-Parisi-Zhang（KPZ）equation，linear equation and Lai-Das Sarma-Villain（LDV） equation, to judge the condition of anomalous scaling behaviors. Analysis shows that within the long wavelength limit the dynamic scaling property of a growth equation is related to the most relevant term, the dimension of the system and noise; and if the anomalous scaling of the equation exists, super_roughening instead of intrinsic anomalous roughening will be displayed in local growth models.