Based on the tight-binding model of the single electron, the 1D model of disordered binary alloy is established, where two different diagonal energies εA and εB are assigned at random to each lattice site and only the short-range hopping integrals between the lattice sites are considered. Using the negative eigenvalue theory and the infinite order perturbation theory, we calculate numerically the eigenvalues and the eigenvectors of the electronic states. The results show that the electronic wave-functions only exist in some narrow region of the system and the localization properties are expected. Using the transfer matrix method, we calculate the localization lengths and discuss how they change with the eigen-energies and the degree of disorder and discuss some characteristics of the localization length with different hopping integral ranges.