Ferroelectrics have a spontaneous polarization that can be switched in direction by applying an external electric field, display coupling between mechanical strain and electric field, and have nonlinear constitutive response. The switchability of ferroelectrics is exploited in the design of non-volatile ferroelectric random-access memories. Since domain walls play an important role in this switching process, the motion of domain walls is critical to the application of high-density non-volatile random-access memory devises. In this research, based on a shell model potential obtained from first principles calculations, molecular dynamics simulations are performed to investigate the domain wall motion of a ferroelectric perovskite under finite temperature and electric field. The process of polarization rotation versus domain wall motion for switching is captured and the domain wall speed has been obtained from the simulation.