A fast, efficient algorithm for computing acoustic fields scattered by inhomogeneous objects in an otherwise homogeneous space is presented. The algorithm, called the Recursive Green’s Function Method (RGFM), constructs the domain Green’s function by recursively combining known Green’s functions from smaller subdomains. The fields on the scatterer surface are then computed using a boundary integral formulation. Proper implementation of the RGFM results in a storage requirement ofO(N)and computational costs ofO(N3/2)andO(N2)for two- and three-dimensional problems, respectively, whereNis the total number of discrete points in the inhomogeneous region. Results are compared with those obtained from exact solutions to show the accuracy of the method.