The present paper treats the problem of the slow motion of a spherical particle, partially immersed in a viscous liquid. It relates to the theory of Brenner and Leal concerning the surface diffusivity of a large Brownian particle and provides important basic information on the so-called "drag-out problem." The numerical investigation yields the local velocity and pressure distribution, the hydrodynamic resistance, and the surface diffusion coefficient, The computations are carried out for low Reynolds and capillary numbers considering a stationary floating macroparticle on a viscous liquid-gas interface, Results are presented for different values of surface dilatational and shear viscosity and contact angles, Brownian motion of the particle is taken into account by integrating the resultant second-order partial differential equations with an alternating direct implicit method. The numerical results reveal for all contact angles a strong decrease of the surface diffusion coefficient when the surface viscosity increases.