The aim of this paper is to propose a new method to solve the inverse scattering problem. This method works directly in the time-dependent domain, using the wave equation and proceeds in two steps. The first step is the Time-Reversed Absorbing Condition ({\em TRAC}) method to reconstruct and regularize the signal and to reduce the computational domain. The second step is the Adaptive Inversion method to solve the inverse problem from the {\em TRAC} data, by using basis and mesh adaptation. This strategy allows to recover the position, the shape and the properties of the scatterer in a precise and robust manner.