We have performed computer simulations of normal grain growth in three-dimension by using the multi-phase-field (MPF) model. For the purpose of the acceleration of computation, we have applied both the active parameter tracking algorithm and parallel coding techniques to the MPF model. The simulation results have been compared with those obtained in previous simulations and a theoretical treatment. We have reconfirmed that the MPF is a powerful tool for simulating grain growth. Especially, the procedure described in this paper is highly efficient.