A novel concept of compressive light field display is proposed by employing a liquid crystal (LC) panel, a projector and a scattering polarizer. Scattering polarizer has characteristics of both transmitting and diffusing in accordance with the polarization state. The polarizing state of output images from LC panel and beam projector is adjusted so that the image from the LC panel is transmitted and the image from the beam projector is diffused by scattering polarizer. Two images originated from both LC panel and projector are observed at different depth positions, simultaneously. Conventional compressive light filed displays have limits to employ high resolution display panels due to diffraction from pixelated structure of LC panels. In the proposed system, drawbacks in conventional system can be mitigated by adopting the scattering polarizer with a projector. Since the scattering polarizer does not have pixel structure, it is possible to combine the high resolution LC panel in the system. Each view image is optimized to target image using simultaneous algebraic reconstruction algorithm. Feasibility of the proposed system is verified with the simulation and the experiment.