The Monte Carlo method is used to simulate ion transport in an Ar plasma electrode sheath with a non-uniform dust. Charge exchange and elastic collisions between ions and neutral atoms and also the collection and Coulomb scattering of ions on the dust particles are examined during the motion of ions in the sheath. In order to study the effect of the non-uniform dust density and size on ion transport, we choose an exponent dust density distribution with a uniform dust size and a normal dust radius distribution with a uniform density and compare the simulation results with those for a uniform dust. It is found that both a non-uniform and a uniform dust density affect the ion density arriving at the electrode significantly and to the same degree. At the same time, it is also found that a non-uniform and uniform dust size influence the ion density arriving at the electrode greatly, but with a slight difference. Therefore, although the dust content is very low in most processing plasmas, its influence becomes evident whether its content is uniform or non-uniform in content and size. So, we can come to the conclusion that the key factors affecting the influence of dust particles on plasma behaviour are the linear density and the average radius of dust particles rather than their distribution.