To extend the recently proposed density functional theory(DFT)methodology to non-uniform non-hard sphere fluid,a new bridge functional as a function of indirect correlation function was proposed,which was b ased on analysis on the asymptotic behavior of the Ornstein-Zernike equation sy stem and the Taylor expansion series whose re-normalization resulted in an adj ustable parameter determined by com bining the new bridge functional wit h the DFT methodology to make the contact density from a single hard wal...