A non-local density functional theory (NLDFT) is used to investigate a mixture of two species of polyelectrolytes which are oppositely charged near a uniformly charged planar surface. In the absence of small ions, we present a systematic study on the effects of surface charge density and the valence of the polyion segments, and the results reveal that little charge inversion occurs except when the polyions existing as counterions bear two charges per segment. With monovalent segments of all polyions, only oppositely-charged polyions can be adsorbed on the surface, it is a neutralization process of the surface charges by the charges born by the adsorbed polyions. The theoretical investigation indicates that the electrostatic correlation mediated by counterions is one of the major underlying forces responsible for the alternating adsorption of oppositely charged polyions.