We calculated the vibrational densities of states for three-dimensional Penrose tiling. Anomalous behaviour at low frequencies is observed. Two crossover frequencies omega _s, and omega _c, exist. The first can be attributed to crossover from surface phonon excitations to bulk phonon excitations, while the second is explained as crossover from phonon excitations to fracton-like excitations. The phonons follow the scaling law omega ^d-1, where d is the Euclidean dimension and equals 3 and 2 for the bulk and the surface phonons, respectively. The fracton-like excitations which have a non-extended character follow the scaling law omega ^ds-1 where d_s is the fracton-like dimension and is shown to equal 3 for the present case.