A new method of data processing is presented for a time-resolved optical computer tomography (CT) imaging of a strongly scattering and weakly absorbing medium, similar to a living body. A fundamental experiment and a numerical calculation of time-resolved spectroscopy are conducted to validate the proposed temporally extrapolated absorbance concept. A numerical simulation shows a possibility of a new method of time-resolved optical CT imaging. A reference cylinder is filled with a uniformly scattering medium, and an object cylinder has a weakly absorbing portion in addition to the uniform scattering in the reference cylinder. The extrapolated values of the difference in the absorbance to the shortest time of flight reduce to the line integrals of the difference in the absorption coefficient along the incident beam lines. By this process, the information of the weak absorption is extracted from the signals subject to the strong scattering, and the extrapolated values provide a set of projection data for a conventional filtered back projection of the CT reconstruction algorithm. The reconstructed image reproduces the difference in the absorption coefficient between the object and the reference with a reasonable accuracy and spatial resolution. This type of image describing the absorption change is useful to noninvasive diagnostics of the oxygen metabolism inside bodies.