One can take advantage of the influence of a polymer conjugated with a protein to control the thermal stability and the deployment of the protein. Here, the structural properties are reported of the protein-polymer conjugate myoglobin (Mb)-poly(ethyl ethylene phosphate) (PEEP) in the native and unfolded conformations, in order to understand the respective roles of the protein and of the polymer size in the stability of the conjugate. The effect is also investigated of the grafting density of the linear biodegradable polyphosphoesters covalently attached to the protein. It is observed that, while the conjugation process at room temperature does not modify the secondary and tertiary structure of the Mb, the unfolding process, as a function of temperature, depends on the grafting density. Small angle neutron scattering reveals that, at room temperature, conjugation does not alter the size of the native protein and that the thickness of the polymer shell around the protein increases as a function of grafting density and of polymer molecular weight. The denatured form of all conjugates is described by an unfolded chain and a correlation length due to the presence of local stiffness.