Grain boundary migration in materials under severe plastic deformation was simulated by the phase field methods. The interface energy and dislocation density on growth kinetics were simulated on systems of 2-dimensional lattice. .In inhomogeneous systems grain size distributions in simulated grain structures were binodal distributions. The classification of the solution of differential equations based on the mean-field Hillert model describing temporal evolution of the scaled grain size distribution function was in good agreement with those given by the Computer simulations. Effect of dislocation on thermodynamic stability was taken into consideration. Dislocation density distribution was calculated by a equation based on the diffusion-reaction equation. Scaled grain size distribution was known to be affected by the dislocation.