The tight binding approximation is one of the most important parts in the teaching of energy band theory，which contains many key concepts of solid state physics and intuitive pictures.Most of the popular textbooks only illustrate the tight-binding approach by using single-band examples.Then it becomes difficult for students to comprehend the Hamiltonian，energy bands，Bloch wave functions and the related concepts.Here a one-dimensional diatomic linear chain is solved with a detailed elucidation for how to obtain the energy bands with multiple orbitals using the tight-binding approximation.The perturbation of atomic energy level and overlap integral of neighboring atomic orbitals are illustrated in the mathematical derivation of the tight-binding Hamiltonian.The energy band dispersion with the relationship to the Bloch wave functions is discussed as well as the factors that determine the number of bands and band widths.