A nonlocal density-functional theory of inhomogeneous ionic fluids proposed by us recently [J. Chem. Phys. 100, 5219 (1994)] for symmetric electrolytes is extended to study the structure of electric double layer for a charge-asymmetric (2:1) situation involving hard sphere ions of equal diameter with a continuum or neutral hard sphere model for the solvent. The hard sphere contributions to the excess free energy density and its derivatives for the inhomogeneous system are evaluated nonperturbatively through a position-dependent effective weighted density, which is also used to obtain the corresponding ionic contributions through a second-order functional Taylor expansion. The calculated results for the continuum solvent model show reasonably good agreement with the available simulation results, while the layering effect due to hard sphere exclusion and the charge inversion phenomena are some of the interesting consequences arising from the molecular nature of the solvent.