This paper presents a space-time stabilized finite element method for the shallow water flow considering moving boundary using the AMR (adaptive mesh refinement) method. The AMR method is introduced to the back-ground mesh in order to improve the numerical accuracy and to treat the geographical topography accurately. The stabilization method based on GLS (Galerin/least-squares) method is employed. The present method is applied to several numerical examples. The efficiency of the present method is shown by numerical results.