An AMR(adaptive mesh refinement) method is presented with different time steps in the cells at inequable levels. In order to get high accuracy in the cells on the interlace, the AMR method is adopted together with the level set method and the ghost fluid method. Euler equations is solved by a WENO algorithm which is easily realized while getting a high resolution. Compared with the method without considering AMR or the level set method, our method shows an advantage in achieving high resolution on the interface. The result indicates that these methods work well together in the numerical simulation.