In the edge plasma, hydrogen and its isotopic molecule will be ionized via collisions with the energetic electrons in the plasmas. The cross section data for the electron impact non-dissociative ion of the hydrogen and its isotopic molecule, which are unavailable from the literature are calculated on the basis of Morse potential function, Franck-Condon theory and semi-classical Gryzinski method. The change of cross section with electron energy and the effect of vibrational level of ground state on the cross section are presented in the paper. The results show that the vibrational excitation plays an important role in the process of ion.