We show that an Ng bridge function modified version of the three-dimensional reference interaction site model (3D-RISM-NgB) solvation free energy method can accurately predict the hydration free energy (HFE) of a set of 504 organic molecules. To achieve this, a single unique constant parameter was adjusted to the computed HFE of single atom Lennard-Jones solutes. It is shown that 3D-RISM is relatively accurate at predicting the electrostatic component of the HFE without correction but requires a modification of the nonpolar contribution that originates in the formation of the cavity created by the solute in water. We use a free energy functional with the Ng scaling of the direct correlation function [Ng, K. C. J. Chem. Phys. 1974, 61, 2680]. This produces a rapid, reliable small molecule HFE calculation for applications in drug design.