We suggest a theoretical method for dealing with the contribution of phasons to the lattice vibration of quasicrystals. Based on this, we derive the density of vibrational states (DOVS) and specific-heat expressions of the icosahedral Al-Mn-Pd quasicrystal, and obtain corresponding numerical solutions which are in agreement with the experimental data measured by Wälti et al. [Phys. Rev. B 57, 10 504 (1998)]. This consistency shows that the contribution of the phasons to either the DOVS or specific heat cannot be neglected at low temperature. Our theory would be also helpful to study further the thermal conductivity of the icosahedral quasicrystal.