A simplified exponential (SEXP) approximation, combining the exponential approximation and the first-order mean spherical approximation, is proposed to improve the equation of state for the Lennard-Jones (LJ) fluid. The SEXP approximation, which can be implemented in an analytical manner, yields better radial distribution functions of the LJ fluid. Extensive comparisons with two typical perturbation theories show that the SEXP approximation is more appropriate to describe the behaviors of the LJ fluid. The latest 33-parameter modified Benedict-Webb-Rubin equation, also calculated, is inadequate in the region of phase coexistence. The SEXP approximation is applied to the calculation of methane properties with much better results than the Peng-Robinson equation of state for saturated liquid densities and second virial coefficients.