Penetration of water molecules into the protein interior under high hydrostatic pressure conditions, leading to protein structural transition, is a well-known phenomenon. The counteracting effect of a naturally occurring osmolyte, trimethylamine N-oxide (TMAO), against pressure-induced protein denaturation is also well-established. But, what is largely unknown is the mechanism by which TMAO counteracts this protein denaturation. So to provide a molecular level understanding of how TMAO protects proteins at high pressure, we report here molecular dynamics (MD) computer simulation results for aqueous solutions of N-methylacetamide (NMA) with different TMAO concentrations over a wide range of pressures relevant to protein denaturation. Hydration behavior of NMA is analyzed at different conditions chosen. It is observed that hydrostatic pressure leads to a significant compression of hydration shell of nonpolar groups and increases hydration number. The compression is relatively insignificant in the vicinity of hydrogen bonding sites. TMAO can prevent pressure-induced enhanced hydration of NMA molecules. Interaction of TMAO with NMA and the structural and dynamical properties of water (site site radial distribution function, coordination number, hydrogen-bond number, and lifetime) are also investigated to find the origin of the counteracting action of TMAO. Our results confirm that TMAO and pressure have counteracting effects on the water structural and dynamical properties, giving an explanation as to how TMAO counteracts pressure-conferred denaturation of proteins.