The properties of surface waves in the partially ionized, incompressible magnetized plasma slab are investigated in the present work. The waves are affected by the non-ideal magnetohydrodynamic (MHD) effects which cause the finite drift of the magnetic field in the medium. When the finite drift of the magnetic field is ignored, the characteristics of the wave propagation in the partially ionized plasma fluid are similar to the ideal MHD, except now the propagation properties depend on the fractional ionization of the medium. In the presence of the Hall diffusion, the propagation of the sausage and kink surface waves depends on the level of fractional ionization of the medium. For example, short wavelength surface modes cannot propagate in the medium if the scale over which Hall operates is comparable to the size of the plasma slab. With the increasing ionization, the surface modes of shorter wavelength are permitted in the system.When both the Hall and Pedersen diffusion are present in the medium, the waves undergo damping. In the case of Pedersen dominating Hall, the damping of the long wavelength fluctuations is dependent on the ratio of the plasma densities inside and outside the slab and on the square of the Pedersen diffusivity. For typical solar parameters, waves may damp over few minutes.