A generalized dual space indicator method is presented for inverse scattering of acoustic waves in a stratified medium.The method is based on the observation that the weighted integration of the measured scattered field can approximate the Greens function very well when source point of  the Greens function is inside the obstacle，but not so well when the source is outside the obstacle. An integral equation whose right-hand side is the Greens function with a source point from a searching region is set up. Then it is known that the norm of the solution of the integral equation has local maximum that lies inside the unknown obstacle

and the region which is surrounded by the local maximal points is exactly the region of obstacle. The most remarkable advantage of this method is that no knowledge of boundary condition is needed.