A two dimensional kinematic frontogenesis process is studied for examing the use of adaptive grids in numerical model. From the comparison of the numerical results using fixed and adaptive grids and those with exact solution, it is found the adaptive runs with 1/3 fewer grid points has the same accuracy, and it can catch the structure of front because of its excellent redistribution of grid points. The results also show the adaptive runs can increase more than 10 hours for the forecasting of extratropical cyclone with the same accuracy comparison to fixed grids. There is an optimum value for grid smoothness and the error increases as the grid orthogonality is considered.