The dynamic scaling properties of growing surfaces with growth inhomogeneities are studied by applying a dy
namic renormalization-group analysis to the generalized Kardar-Parisi-Zhang(hereafter abbreviated to KPZ) equation,
which contains an additional term of growth inhomogeneities. In a practical crystal growth process, these growth inho
mogeneities can be induced by surface impurities and defects and are modeled by a screened Coulomb function in this
paper. Our results show that the existence of the growth inhomogeneities can significantly change the dynamic scaling
properties of a growing surface and can lead to a rougher surface.