The propagation of dust-acoustic solitons in an inhomogeneous plasma is studied for the case in which the equilibrium dust density is a constant but the equilibrium dust charge is spatially nonuniform and determined by the self-consistent charging equation. It is shown that the amplitude of the solitons is inversely proportional to the one-fourth power of the equilibrium dust charge number and only compressive solitons exist in this case. When the soliton propagates from high to low density regions, its amplitude and width increases with distance while its velocity shows complex variations. The spatial distribution of the relative amplitude of the dust density perturbation exhibits a transition from decrease to increase, which differs significantly from that of the potential perturbation.