Abstract: The time dependent energy spectra of acclerated particles in Fermi accleration by shock waves have been calculated for various momentum distributions of source particles and parameters. It is shown that the high energy parts of acclerated particles spectra are power-law forms in the enough long time, no matter what the momentum distribution is possessed by source particles. But the time evolution of energy spectrum of acclerated particles depends on the momentum distribution of source particles. Therefore it is unsuitable for a transient shock process that the energy spectra of acclerated particles are represented by power-law form with constant index.