We present a new integral equation for the radial distribution function of classical fluids. It employs the bridge function for a short-range repulsive reference system which was used earlier in our dense fluid perturbation theory. The bridge function is evaluated using Ballone et al.’s closure relation. Applications of the integral equation to the Lennard-Jones and inverse nth-power (n=12, 9, 6, and 4) repulsive systems show that it can predict thermodynamic and structural properties in close agreement with results from computer simulations and the reference-hypernetted-chain equation. We also discuss thermodynamic consistency tests on the new equation and comparisons with the integral equations of Rogers and Young and of Zerah and Hansen. The present equation has no parameter to adjust. This unique feature offers a significant advantage as it eliminates a time-consuming search to optimize such parameters appearing in other theories. It permits practical applications needing complex intermolecular potentials and for multicomponent systems.