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An analysis using the lubrication approximation is performed for the dispersion of a neutral non-reacting solute due to electroosmotic flow through a circular channel under the combined effects of longitudinal non-uniformity of potential and hydrodynamic slippage on the channel wall.The wall is periodically patterned for the charge and slip distributions, with a wavelength much longer than the channel radius.It is shown that the presence of slip can greatly amplify the increased dispersion caused by induced pressure gradient brought about by the non-uniformity of wall potential.Non-uniform wall potential interacting with non-uniform slip can give rise to effects much different from those when the potential and slip are both uniformly distributed and equal to the averages of the non-uniform distributions.