Imaging objects hidden by turbid media, such as smoke, fog, or biological tissues, is a challenge for scientists. Compressive ghost imaging and a photometric stereo approach are employed to estimate the 3D shape of an object behind a scattering medium. A sequence of speckle patterns is projected onto the object. Four images with different shadings are accurately reconstructed from the object behind a diffuser. The 3D shape is obtained by applying the photometric stereo to the reconstructed 2D images. This technique is robust against scattering, even for 3D imaging in opaque media with multiple scattering, and it is not sensitive to changes in the scattering media or displacement of the medium. Also, it has the benefits of compressive ghost imaging strategy, such as hyperspectral or polarimetric imaging with sub-Nyquist sampling. As a proof for this concept, the 3D shape of a target behind a diffuser was experimentally retrieved, and the results were compared with the original 3D shape and the 3D shape reconstructed in the absence of the diffuser. The accuracy of the reconstructed 3D shapes was maintained in the presence of the diffuser plate in various thicknesses and orientations.