In this paper, nonequilibrium molecular dynamics simulations were performed on a single component 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine lipid bilayer in order to investigate the thermal conductivity and its anisotropy. To evaluate the thermal conductivity, we applied a constant heat flux to the lipid bilayer along and across the membrane with ambient water. The contribution of molecular interaction to the heat conduction was also evaluated. Along the bilayer plane, there is little transfer of thermal energy by the interaction between lipid molecules as compared with the interaction between water molecules. Across the bilayer plane, the local thermal conductivity depends on the constituents (i.e., water, head group, and tail group of lipid molecule) that occupy the domain. Although the intramolecular transfer of thermal energy in the tail groups of lipid molecules works efficiently to promote high local thermal conductivity in this region, the highest thermal resistance appears at the center of lipid bilayer where acyl chains of lipid molecules face each other due to a loss of covalent-bond and low number density. The overall thermal conductivities of the lipid bilayer in the directions parallel and perpendicular to the lipid membrane have been compared, and it was found that the thermal conductivity normal to the membrane is higher than that along the membrane, but it is still smaller than that of bulk water.