Using a kinetic model for low-frequency dust acoustic waves (DAW) in a dusty plasma, we have examined the effects of a dust-size distribution on their propagation and damping. Both Landau damping and damping due to dust-charge variation are included. We consider Gaussian and power-law dust-size distributions. In accordance with earlier results of Melandsø et al., we find that the dust Landau damping dominates at short wavelengths. At wavelengths longer than the Debye length λD0, the dust-charge variation is generally dominant. It is always dominant for the power-law size distributions that we have studied. We also find that if the upper and lower size limits of the dust are chosen so that the average dust size remains constant, regardless of the power-law exponent γ, the wave properties are practically identical to those of a monosize distribution of the average dust size. For a Gaussian dust-size distribution, Landau damping may be the dominant damping mechanism if the dust plasma is tenuous (P[Lt ]1) and the width of the distribution is large.