The influence of magnetic field strength, ion mass, and the non-thermal character on the dispersion properties of ion-cyclotron surface wave is investigated in a semi-bounded (r, q) distribution dusty plasma. In the limit of short wave number, the dispersion relation is derived by adopting the specular reflection boundary condition and the effective screening distance in (r, q) distribution dusty plasma. It is found that the stronger magnetic field strength suppresses the wave speed, but the heavier ions will enhance the wave propagation. To investigate the wave propagation in the non-Maxwellian plasma, the typical values of r and q are chosen and the dispersion relation is plotted to obtain the general character of wave propagation. The result would reduce to the case of Maxwellian plasma for r→0 and q→∞.