Lipid bilayers grafted with polyethylene glycol (PEG) of different sizes (M-w = 750, 2000, and 5000) and grafting densities (1.6-25 mol % of PEGylated lipid in dipalmitoylphosphatidylcholine (DPPC) lipid molecules) were simulated with human serum albumin (HSA) using coarse grained force fields. At low enough grafting density, the PEG has a conformation similar to that of an isolated chain in water, and its Flory radius R-F is smaller than the distance between the grafting points (d), which is the so-called "mushroom" regime. In contrast, densely grafted PEG chains (R-F > d) extend like brushes, with brush layer thickness given by the Alexander-de Gennes theory. A nearly spherical HSA added to this simulation migrates to the bilayer surface because of the charge interactions between anion residues of HSA and cationic cholines of DPPC, but this HSA-bilayer binding can be sterically suppressed by the PEG chains to an extent that depends on the PEG size and grafting density. In particular, regardless of the extent of the coverage of the PEG on the bilayer, the binding between HSAs and bilayers is suppressed by the PEG layer in a brush but not in a mushroom, indicating that the attractive force between proteins and bilayers can overcome the steric effect of the PEG layer in the mushroom state or in the transition region from mushroom to brush. This helps explain and clarify experiments that show much less adsorption of plasma proteins onto the particle or membrane surface when PEGs are in the brush rather than in the mushroom state.