This paper studies the reconstruction of the absorption properties of a dense scattering medium from time-resolved data. A Progressive Expansion (PE) Algorithm, similar to a layer-stripping approach, has been developed. The method progressively evaluates increasing depths within the medium by successively considering signals entering the detector at increasing time following an incident pulse. In order to reduce the propagation of reconstruction errors occurring at shallower depths, an overlapping scheme is introduced which uses readings from several consecutive time intervals in the reconstruction. In each overlapping time interval, the region under consideration is solved using a perturbation approach recently described by our group. The proposed algorithm is applied to several inhomogeneous media containing simple structures. Two sets of data have been tested: one calculated according to the perturbation model; and the other by Monte Carlo simulations. The results show that the PE method, when combined with proper overlapping, can make effective use of the time-resolved data. Compared to our previous results with steady-state data, the present methods can probe deeper below the surface and produce a more accurate estimate.