Abstract: By using a classical screened Coulomb potential with two phase factors and adopting classical analytical methods, the predictive descriptions on the energy level and spectrum of anti-hydrogen atom are given. As a result, the great differences of the energy level and spectrum between anti-hydrogen atom and hydrogen atom are found. The main quantum number n is a fraction less than 1 and the spectrum of the anti-hydrogen atom occurs only when the positron transits from ground state to excitation state, which is just contrary to the luminescent mechanism of an hydrogen atom.