The sorption process of a system with a power relation between diffusivity and concentration is investigated by a numerical solution of diffusion equation for a slab based on a dissolved solid coordinate with uniform initial concentration, normalized by a constant surface concentration. The sorption curve, concentration profile, ratio of average to center concentration, and sorption rate, are analyzed for various power index values and initial concentrations. Finding a regular regime in the later stage in which the sorption rates become independent of initial concentrations, a semi-analytical solution for this regime is derived and satisfactory agreement is found between the analytical solutions and the numerical results. The apparent diffusion coefficients and the corresponding apparent concentrations, based on the analytical solutions for constant diffusion coefficient, are calculated for both the initial stage and the regular regime of the sorption process. The apparent concentrations are related to the power index and the normalized initial concentration or the average concentration. The relations are useful for easy determination of the concentration-dependent diffusion coefficient as a function of concentration for the sorption experiments with step change of initial and surface concentrations.