The natural environment of proteins is a crowded environment as in cells, extracellular fluids, or during processing. Semidilute polymer solutions have been a source of rich structural and dynamical properties and mimic a crowded environment, but a proper understanding of protein-dynamics in the crowded environment is far lagging. Such a study not only realizes protein's natural environment in a crowded solution in the cell or during processing but also manifests the underlying protein polymer interaction. By dispersing model globular proteins like alpha-lactalbumin (La) and hemoglobin (Hb), in aqueous solution of poly(ethylene oxide) (PEO) we mimic a crowded environment and use state-of-the-art neutron spin echo (NSE) and small-angle neutron scattering (SANS) techniques to observe the corresponding protein dynamics in semidilute polymer solution. NSE can access the fast diffusion process (D-fast) prior to the slow diffusion process on long times and length scales (D-gamma). The protein dynamics in a crowded environment can be described analogous to the diffusion in a periodic potential. The fast dynamics corresponds to diffusion inside a trap built by the polymer mesh while the slower process is the long time diffusion on macroscopic length scales also observed by other techniques. We observe the onset of fractional diffusion for higher concentrated polymer solutions.