We report a distorted Born iterative method (DBIM) for the acoustic seismic inversion problem. The method makes use of a renormalization of the Lippmann-Schwinger equation (LSE) to a Volterra form that resolves the convergence issue with the causal forward Born series. It has potential advantages over other inverse methods. In contrast to the causal scattering series methods, the DBIM avoids expanding the velocity perturbation in terms of orders of the data. Compared with FWI, the DBIM has less dependence on an accurate starting velocity model, and has little possibility of encountering a local minimum. A 1-D numerical test shows that the DBIM can yield a good estimation of the velocity with only a few iterations.