Multi-dimensional laser cooling of heavy-ion beams at the cooler storage ring S-LSR in Kyoto University is studied numerically using the molecular dynamics simulation technique in which the stochastic interaction between ions and laser photons is incorporated. The purpose of the study is to find out how low-temperature we can achieve using actual experimental parameters and to verify the observation result in the experiment. In these proceedings, the characteristics of the ion beam lasercooled in S-LSR are reported. It has been confirmed that, in spite of the limitation in the experimental conditions such as a single laser beam, low power, fixed detuning and short laser-cooling section, the three-dimensionally low-temperature beam is obtained through resonant coupling at a low intensity of 10 ions in the ring, which is consistent with the experimental result. It is also demonstrated that a string crystalline state of the beam can be formed at a further lower intensity.