This paper investigates the propagation of linear dust acoustic waves in inhomogeneous dusty plasmas due to spatial gradients of dust charge, plasma densities. A linear dispersion relation is obtained with the non-adiabatic dust charge fluctuation and the non-thermally distributed ions. The numerical results show that the inhomogeneity, nonthermal ions and non-adiabatic dust charge fluctuation have strong influence on the frequency and the damping rate of waves.