A new bridge functional as a function of indirect correlation function was proposed, which was based on analysis on the asymptotic behavior of the Ornstein-Zernike (OZ) equation system and a series expansion whose renormalization resulted in an adjustable parameter determined by the thermodynamics consistency condition. The proposed bridge functional was tested by applying it to bulk hard sphere and hard core Yukawa fluid for the prediction of structure and thermodynamics properties based on the OZ equation. As an application, the present bridge functional was employed for non-uniform fluid of the above two kinds by means of the density functional theory methodology, the resulting density distribution profiles were in good agreement with the available computer simulation data.