We investigate the electronic state of the periodic Anderson-Holstein model, which includes both the electron-electron Coulomb interaction and the electron-phonon coupling, away from half filling. The model is solved by using the dynamical mean-field theory combined with the exact diagonalization method. The heavy fermion state with large effective mass due to the electron-phonon coupling is realized in the wide range of the f-electron number n(f), while that due to the Coulomb interaction is realized in the narrow range of n(f)similar to 1. (c) 2006 Elsevier B.V. All rights reserved.