Nonequilibrium molecular dynamics simulations are carried out on single component lipid bilayers with ambient water in order to investigate the effect of acyl chain length on heat transport characteristics along and across the membranes. In this study, dipalmitoyl-phosphatidyl-choline (DPPC), dilauroyl-phosphatidyl-choline (DLPC), and stearoyl-myristoyl-phosphatidyl- choline (SMPC) which has two acyl chains of both sixteen C atoms, both twelve C atoms, and eighteen and fourteen C atoms, respectively, were used as lipid molecules. In the direction along the membranes, thermal conductivity corresponds with that of each membrane. On the other hand, in the direction across membrane, the highest thermal resistance exists at the center of lipid bilayer where lipid acyl chains face each other. However, asymmetric chain length reduces thermal resistance at the interface between lipid monolayers. Therefore, thermal conductivity across the membrane which consists of asymmetric chain length is higher than those which consist of symmetric chain length.