Abstract: With the extension rule of the method of approximate values of Dirac δ function a new regularization equation of vacuum polarization （self-energy） for photons is developed with （n ↑ ） as the regularization parameter which has the same dimension as 4-momentum, the equation is similar to that in reference books such as that of dimensional regularization. The separate amplitudes of tree-level and l-loop contributions of the system are determined, the counterterm and the renormalized amplitudes are further derived while the latter is all the same to that in reference books. Finally the counterterm Lagrangian is determined.

Key words: quantum field interactions, vacuum polarization for photons, ultra-violet divergence, Diracδ function