In this paper, a modified 3D computational reconstruction method in the compressive 4D-spectro-volumetric snapshot imaging system is proposed for better sensing spectral information of 3D objects. In the design of the imaging system, a microlens array (MLA) is used to obtain a set of multi-view elemental images (EIs) of the 3D scenes. Then, these elemental images with one dimensional spectral information and different perspectives are captured by the coded aperture snapshot spectral imager (CASSI) which can sense the spectral data cube onto a compressive 2D measurement image. Finally, the depth images of 3D objects at arbitrary depths, like a focal stack, are computed by inversely mapping the elemental images according to geometrical optics. With the spectral estimation algorithm, the spectral information of 3D objects is also reconstructed. Using a shifted translation matrix, the contrast of the reconstruction result is further enhanced. Numerical simulation results verify the performance of the proposed method. The system can obtain both 3D spatial information and spectral data on 3D objects using only one single snapshot, which is valuable in the agricultural harvesting robots and other 3D dynamic scenes.