Extremophiles adopt strategies to deal with different environmental stresses, some of which are severely damaging to their cell membrane. To combat high osmotic stress, deep-sea organisms synthesize osmolytes, small polar organic molecules, like trimethylamine-N-oxide (TMAO), and incorporate them in the cell. TMAO is known to protect cells from high osmotic or hydrostatic pressure. Several experimental and simulation studies have revealed the roles of such osmolytes on stabilizing proteins. In contrast, the effect of osmolytes on the lipid membrane is poorly understood and broadly debated. A recent experiment has found strong evidence of the possible role of TMAO in stabilizing lipid membranes. Using the molecular dynamics (MD) simulation technique, we have demonstrated the effect of TMAO on two saturated fully hydrated lipid membranes in their fluid and gel phases. We have captured the impact of TMAO's concentration on the membrane's structural properties along with the fluid/gel phase transition temperatures. On increasing the concentration of TMAO, we see a substantial increase in the packing density of the membrane (estimated by area, thickness, and volume) and enhancement in the orientational order of lipid molecules. Having repulsive interaction with the lipid head group, the TMAO molecules are expelled away from the membrane surface, which induces dehydration of the lipid head groups, increasing the packing density. The addition of TMAO also increases the fluid/gel phase transition temperature of the membrane. All of these results are in close agreement with the experimental observations. This study, therefore, provides a molecular-level understanding of how TMAO can influence the cell membrane of deep-sea organisms and help in combating the osmotic stress condition.