In this work,a bridge density functional approximation(BDFA)(J.Chem.Phys.112,8079(2000))for a non-uniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa(HCRY)fluid.It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid.A new bridge functional approximation is proposed,which can accurately predict the radial distribution function of the bulk HCRY fluid.With the new bridge functional approximation and its associated bulk second order direct correlation function as input,the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying exteal fields,and the theoretical predictions are in good agreement with the corresponding simulation data.The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase,and the adsorption properties of the HCRY fluid,which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail.