Grafted polymers oil the surface of lipid membranes have potential applications in liposome-based drug delivery and Supported membrane systems. The effect of polymer grafting on the phase behavior of bilayers made up of single-tail lipids is investigated using dissipative particle dynamics. The bilayer is maintained in a tensionless state using a barostat. Simulations are carried Out by varying the grafting fraction, G(f), defined as the ratio of the number of polymer molecules to the number of lipid molecules, and the length of the lipid tails. At low G(f), the bilayer shows I sharp transition from the gel (L-beta) to the liquid-crystalline (L-alpha) phase. This main melting transition temperature is lowered as G(f) is increased, and above a critical value of G(f), the interdigitated L-beta I phase is observed prior to the main transition. The temperature range over which the intermediate phases are observed is a function of the lipid tail length and G(f). At higher grafting fractions, the presence of the L-beta I, phase is attributed to the increase in the area per head group due to the lateral pressure exerted by the polymer brush. The areal expansion and decrease in the melting temperatures as a function of G(f) were found to follow the scalings predicted by the self-consistent mean field theories for grafted polymer membranes. Our study shows that the grafted polymer density can be used to effectively control the temperature range and occurrence of a given bilayer phase.