The relation between domain wall motion and intensity of driven current is examined in a phenomenological theory where the kinetic energy is expanded as a series of polynomial function of current density just as the Landau phase transition theory. The dependency of velocity on current density is square root which degenerates into linear if the current is much higher than the critical value. The theory result is consistent with several previous experiments and also can explain the change of critical current in the presence of temperature. The role of temperature playing in the dynamics of domain wall motion is also discussed. The phase transition theory in terms of current density is employed to explain the critical behavior of domain wall motion.