Based on the functional integral procedure, a recently proposed bridge density function [J. Chem. Phys. 112 (2000) 8079] is developed to calculate global thermodynamic properties of non-uniform fluids. The resulting surface tension of a hard wall-hard sphere interface as a function of the bulk hard sphere fluid density is in good agreement with the available simulation data. The proposed numerical procedure from the approximation of non-uniform first=order direct correlation function to a non=uniform system with excess Helmholtz free energy is of fundamental importance for phase behaviour under the confined condition due to the fact that many available simple approximations in classical density functional theory are for non=uniform first=order direct correlation function.