The nonuniform first-order direct correlation function (DCF) for a hard-core attractive Yukawa model fluid (HCAYMF) was expanded around bulk density and truncated at the lowest order. The truncation was made formally exact by applying the functional counterpart of Lagrangian theorem of the differential calculus to the functional expansion. To calculate the density profile of a nonuniform HCAYMF, the uniform second-order DCF from the mean spherical approximation for HCAYMF was employed; the resulting density functional theory (DFT) was computationally simpler and quantitatively more accurate than the previous weighted density approximation (WDA) + functional perturbation expansion approximation (FPEA) DFT, which divided the interaction potential into a short-ranged hard-sphere-like part and a long-ranged interaction part and treated the former by the WDA and the latter by third-order FPEA. The present DFT also was employed to calculate the radial distribution function of bulk HCAYMF and bulk hard-sphere fluid;, the calculated results were in good agreement with simulation data.