Electron-impact theoretical cross sections and rate coefficients for vibrational excitation of vibrationally excited H molecules, occurring through the H resonant species in the Rydberg-excited electronic state, are presented. The cross sections are calculated as functions of the incident electron energy by adopting the local-complex-potential model for resonant collisions and by using ab initio calculated molecular potentials and resonance widths. The calculations have been extended to all possible vibrational transitions linking all 15 vibrational levels of the electronic ground state of the H molecule. The corresponding rate coefficients are also obtained as a function of the electron temperature by assuming a Maxwellian electron energy distribution function, and a simple analytical expression is derived. Finally, the present rate coefficients for the transitions starting from the lowest vibrational level of the H molecule are compared with those for the process involving the resonant state of the H molecular ion.