The photodissociation process of argon cluster ions is studied by using Tully's molecular dynamics with quantum transition method. It is demonstrated that the nonadiabatic transition plays an important role in the process. A lifetime of an initial photoexcited state and recovery time to the electronic ground state are obtained for several cluster sizes and excitation energies. A decay curve of the photoexcited state is composed of a Gaussian-type decay followed by an exponential decay. The initial Gaussian-type delay of the decay is attributed to the acceleration time of the nuclei. The recovery to the ground state is slower for the higher excitation energy, which is due not only to the increased number of the nonadiabatic transitions, but to the lower rate of each transition. The low recovery rate at the higher excitation energy might be explained from the low density of states in the energy range.