We investigate a heavy fermion behaviour and a deformation of an effective potential of the ions due to electron-phonon interaction for the periodic Anderson-Holstein model by using the dynamical mean-field theory combined with the exact diagonalization method. For the strong electron-phonon coupling, the system shows an anomalous heavy fermion behaviour with a large lattice fluctuation and an extreme phonon softening, and then an effective potential for the ions changes from a simple harmonic potential for the non-interacting case to a double-well potential for the strong electron-phonon coupling. (c) 2006 Elsevier B.V. All rights reserved.