The propagation of solitons in an inhomogeneous dusty plasma composed of two kinds of dust grains with different masses is investigated by using the reductive perturbation technique. In the lowest order, if the interface of the two kinds of dust grains is discontinuous, the transmission and reflection waves can be both described by the KdV equation. The numbers and amplitudes of both transimtted and reflected solitons from an incident soliton are given analytically for this case. If the interface of the two kinds of dust grains is continuous, neglecting the reflection, the nonlinear dust acoustic wave can be described by a KdV-type equation in the lowest order. The amplitudes, propagating velocities of these quasi-solitons for this case are also given analytically in this paper.