Abstract: A new method for adaptive refinement of 2D unstructured grids generated by advancing front technique is presented.Some small triangle units are arranged on the place where mesh needs to be refined,and all the sides of these units are regarded as a part of the initial front.During the advancing process,near the above mentioned units,the cells are naturally generated from small to large.For the flow with shock,in the mesh graph,a quite clear shock picture is formed.