Many biomedical applications employ covalent attachment to synthetic polymers to enhance the efficiency of proteins or other therapeutically active molecules. We report here the impact of polymer conjugation on the structural and thermal stability of a protein model, the bovine serum albumin, using a variable number of linear biodegradable polyphosphoesters, which were covalently tethered to the protein. We observed that BSA's secondary structure measured by circular dichroism is independent of the conjugation. Small-angle neutron scattering, however, reveals a change from ellipsoid to globular shape of the whole complex arising from a slight compaction of the protein core and an increase of the polymer's radius of gyration as a function of the grafting polymer density. In particular, we highlight a gradual change of the polymer conformation around the protein and elongation of the semimajor dimension of the ellipsoidal protein. Our results will contribute to the description of biophysical characteristics of a new class of biologically relevant protein-polymer conjugates.