Using atomistic computer simulations, we study the adsorption of different globular protein fragments with different secondary structures on the surface of a hydrophilic glassy polymer, poly(vinyl alcohol), or PVA, and compare the results with our earlier calculations on hydrophobic graphite. The simulations were mainly carried out with implicit solvent in an effective dielectric medium by energy minimizations and molecular dynamics at room temperature. We find that on the hydrophilic PVA surface the fragments basically retain their globular shape with an incomplete denaturation, at variance with our earlier results for the same fragments on graphite. Correspondingly, the interaction energy between the fragments and the surface is significantly smaller than on graphite, both because less residues are in contact with the surface, and because they interact more weakly. Moreover, very few hydrogen bonds are formed between the adsorbate and the PVA surface, since both the protein fragments and the polymer chains separately optimize these interactions. Additional molecular dynamics simulations in explicit solvent were also performed to study the hydration of the adsorbed fragments and to estimate the possible solvation effects.