In strong laser fields, the unperturbed ground electronic state is not the true ground state any more. The electronic states are mixed strongly, depending on both the polarization and amplitude of laser fields. This distortion effects of the initial electronic states on the tunneling photo-ionization are taken into account within our generalized Keldysh theory. We show that including the distortions leads to the quantitative reproduction of the exact numerical calculations of the ionization rate for hydrogen atom reported by Brabec and co-workers [A. Scrinzi, M. Geissler, T. Brabec, Phys. Rev. Lett. 83, 706 (1999)]. (c) 2005 Elsevier B.V. All rights reserved.