A simple perturbative density functional approach has been developed for an inhomogeneous fluid mixture based on a functional Taylor expansion of the free energy in terms of the density inhomogeneity up to third order. A new approximation for the three-body correlation function for the mixture is proposed and the theory is applied to predict the structure of hard-sphere mixture near a hard wall. The calculated density profiles for both the components are found to agree quite well with the corresponding computer simulation results. This theory for an inhomogeneous fluid is also applied to study the structure of a homogeneous hard-sphere mixture, for which the calculated radial distribution functions are found to compare well with the corresponding results obtained from the Fourier transform of the structure factors from the Percus-Yevick theory of liquid mixtures.