The conventional two-layered, alongshore independent, wind-driven upwelling model is extended to incorporate an initial subsurface current, through the advective term involving cross-stream shear. Under the condition that the thickness of the upper layer and the equilibrium displacement of the interface are both much smaller than the thickness of the second layer, explicit solutions are obtainable for cases of exponential and parabolic profiles of the initial interface. In the presence of the initial current in the lower layer, the upwelling is reduced near the coast, and increased offshore compared to a case without the initial current. The modification is achieved through an abatement and an enhancement in divergence near the coast and offshore, respectively, as a result of the net effect from the continuity condition and the advection of the offshore velocity in terms of the cross-stream shear. The mechanism provides one of the possible explanations for an exceptionally wide cold water zone observed in an upwelling system influenced by an ambient large-scale ocean current. ¿ American Geophysical Union 1992