An accurate adaptive mesh refinement based on the CIP method is proposed and It is applied to solve the two dimensional advection equations In tins method, the level set function is employed to refine and merge the computation cells To enhance the accuracy of the solution, the spatial discretization is made by the CIP method The ClP method has many advantages such as the thud order accuracy, less diffusivity, and shape conserving. The mathematical formulation and numerical results are also described. To verify the efficiency, accuracy, and capability of the proposed algoritlun, two dimensional rotating slotted cylinder and Idealized frontogenesis are numerically simulated by the present scheme. As results, It is confirmed that the present method gives an efficient, reasonable solution In the advection equation<br/>