We employ an analytical approach introduced by López to determine the anomalous scaling exponent of the growth equation with a generalized conservation law in both the weak-and strong-coupling regimes, which included the Kardar-Parisi-Zhang（KPZ）, Sun-Guo-Grant（SGG）, and molecular beam epitaxy （MBE）equations as special cases and allows for a unified treatment of growth equations. Analysis shows that KPZ equation and SGG equation exhibit normal Family-Vicsek scaling behavior, whether in the weak-coupling or strong-coupling regime. Differently, MBE equation exists intrinsic anomalous scaling in the strong-coupling regime and normal Family-Vicsek scaling behavior in weak coupling regime. All the conclusions obtain here are well consistent with the corresponding results derived by the dynamic renormalization group theory, numerical simulation and experiment.