In a high-intensity laser field an atom can absorb more photons than the minimum necessary for ionization. It is known as above threshold ionization (ATI). Theoretically it is the most difficult case to handle as we have to consider transitions in continuum. To study ATI we use the perturbation theory and Green's function formalism. We have derived the modified two-term Coulomb Green's function (CGF) Sturmian expansion. In each term explicit summation over all intermediate states is carried out. The transition amplitude may be obtained in a closed form. The generalized cross sections are evaluated for the photoionization of atomic hydrogen in ns states with up to four excess photons. Calculations are performed in a wide range of wavelengths for linear and circular polarization. In the cases for which data are available, our results agree very well with the previous ones.