The effects of the dust density nonuniformity and the polarization force on linear propagation of the dust-acoustic waves in a nonuniform dusty plasma (consisting of electrons, ions, and arbitrarily charged dust particles) have been theoretically investigated. It has been shown that the linear dispersion properties of the dust-acoustic (DA) waves have been significantly modified by the dust density nonuniformity, dust polarity, and the polarization force. It is also found here that the phase speed of the DA waves is decreased by the effects of polarization force, and that their amplitude increases with the decrease of equilibrium dust number density. The different situations, which are relevant to different space and laboratory dusty plasmas, have been briefly discussed.