A tight-binding model is presented to study the density-of-states and some other electronic properties of a liquid metal and an amorphous solid composed of atoms with one-atomic orbital per site. A one-electron Green function is expanded in terms of atomic orbitals and described by a perturbation expansion series in powers of H'mn≡Hmn+ωSmn, Hmn and Smn being a non-diagonal matrix element of Hamiltonian and an overlap integral, respectively, while ω designates the energy. An extended chain approximation is introduced in order to express atomic correlation functions by means of a radial distribution function g(Rmn). The ensemble-averaged Green function is evaluated based upon the single-site theory of Matsubara and Toyozawa, by which a short-range order of atomic configuration in a liquid metal and an amorphous solid is most properly taken into account. It is mentioned that the present theory is applicable to liquid transition metals and to alkali metals under a supercritical condition. The non-self-consistent treatment in our scheme is shown to be equivalent to the moment-expansion method of Cyrot-Lackmann. In actual implementation of numerical calculation, both the non-self-consistent and self-consistent approximations in our theory are applied and the complete set of atomic orbitals is assumed to be quasi-orthogonal, i.e., Smn=δmn. As a pair correlation g(Rmn), we employ three models: (1) A random liquid, (2) a hard-core-random liquid and (3) a hard-core-modified liquid; and one real liquid case; the experimental value of Ni at T=1500 °C. The effect of a short-range order in the atomic configuration on the density-of-states, etc., is discussed.