This doctoral thesis presents a newly developed density functional theory (DFT), i.e., the weighted correlation approach (WCA), to study the structural and thermodynamic properties of an inhomogeneous fluid at an interface. The WCA approach provides a generic formulation to evaluate the change of the single-particle direct correlation function in terms of a series of pair direct correlation functions weighted by different correlation-weight functions with adjustable correlation-weight factors. When applied practically, however, an approximation of the pair direct correlation function has to be made, together with appropriate definitions of the weighted densities and the choices of the correlation-weight functions. Despite this seeming complexity, it is shown that the WCA approach can be regarded as a generalization of the classic density functional approaches and this enables us to develop and apply DFT methods in different ways. For demonstration purposes, several implementations of the WCA approach are proposed and applied to predict the density distribution of an inhomogeneous fluid at an interface. The WCA approach is also employed with a novel pressure expression to investigate the inhomogeneous fluid-mediated interaction pressure for different cases. The WCA calculations from the above applications suggest that it is a successful approach for describing the structural and thermodynamic properties of an inhomogeneous fluid at an interface, as compared to the published results of the Monte Carlo simulations, density functional methods and experimental data.