A quasi-3-D inverse scattering technique is proposed to reconstruct sound velocity slices of the weak scattering tissues by transmitting and receiving acoustic waves around a single rotational axis. The reconstructing procedure proposed is as follows. First, a backpropagation operation is introduced using the holographic formula for a homogeneous medium. This backpropagation preprocessing operation contributes dramatically to the reduction of the final quantitative reconstruction errors. Next, after the Rytov transform over the marginal backpropagated plane, data are then filtered in the perpendicular direction to discriminate the horizontally scattered wave. Consequently, quasi-3-D sound velocity images on the horizontal sliced plane of an object can be obtained, using the conventional 2-D inverse scattering reconstruction procedure. Precision of the proposed 3-D reconstructed sound velocity image is investigated using the calculated scattered data from the spherical object. As a result, it is demonstrated that quantitative precision of the reconstructed 3-D velocity image is verified to be within 1% over the range of the velocity inhomogeneity from -10% to 10%. The results obtained are promising for actual clinical applications such as the human breast cancer screening test.