Molecular dynamics (MD) simulations with a coarse-grained model are applied to investigate the binary adsorption of proteins onto an ion-exchange chromatographic medium. In particular, the adsorption of human serum albumin (HSA) and bovine hemoglobin (bHb) on the anion exchanger Q Sepharose FF is studied. Simulations with different initial orientations of the proteins and different protein-protein distances are carried out over a 2000 ns time scale. The protein-ligand potential energies and protein-ligand minimum distances are analyzed, and stable adsorption of HSA but no stable adsorption of bHb is observed. Interactions between HSA and bHb as well as a coupled movement of these two proteins are observed in all simulations. Because of the interaction between these two proteins, their rotations and adjustments to reach a favorable adsorption configuration are hindered. The competition is further indicated by changing adsorption sites on the HSA surface. The interaction and aggregation of the two proteins are investigated in detail.