The cathodic polarization of a copper electrode in CuCN/KCN solution was interpreted by considering the diffusion and migration of all ionic species, chemical reactions involving cyano-copper(I) complexes, and the quasiequilibrium of charge transfer reaction. Experimental polarization curves were compared with theoretical ones, where the diffusion layer thickness was determined. The present model was applied to the prediction of thickness distribution of copper coating on grooved substrates. Two types of substrates with grooves of different size (width x depth), (a) 5 mm x 5 mm and (b) 1 mm x 1 mm, were used. Agreement between theory and experiment was satisfactory for substrate a, but not for substrate b. The effect of convective mass transfer in the groove was discussed.