An integral equation theory for the Lennard-Jones fluid is investigated using a proposed new closure based on a modification of the Verlet-modified bridge function, which has been known to be very successful for hard body fluids. The structural and thermodynamic properties of the Lennard-Jones fluid calculated from this integral equation theory over a wide range of temperature and density show very good agreement with those obtained from simulation or from equation of state derived from simulation data. The gas-liquid phase diagram predicted by the present integral equation theory is shown to agree quite well with the corresponding simulation results.