Objective: Stimulated Raman projection tomography (SRPT), a recently developed label-free volumetric chemical imaging technology, has been reported to quantitatively reconstruct the distribution of chemicals in a three-dimensional (3D) complex system. The current image reconstruction scheme used in SRPT is based on a filtered back projection (FBP) algorithm that requires at least 180 angular-dependent projections to rebuild a reasonable SRPT image, resulting in a long total acquisition time. This is a big limitation for longitudinal studies on live systems. Methods: We present a sparse-view data-based sparse reconstruction scheme, in which sparsely sampled projections at 180 degrees were used to reconstruct the volumetric information. In the scheme, the simultaneous algebra reconstruction technique (SART), combined with total variation regularization, was used for iterative reconstruction. To better describe the projection process, a pixel vertex driven model (PVDM) was developed to act as projectors, whose performance was compared with those of the distance driven model (DDM). Results: We evaluated our scheme with numerical simulations and validated it for SRPT by mapping lipid contents in adipose cells. Simulation results showed that the PVDM performed better than the DDM in the case of using sparse-view data. Our scheme could maintain the quality of the reconstructed images even when the projection number was reduced to 15. The cell-based experimental results demonstrated that the proposed scheme can improve the imaging speed of the current FBP-based SRPT scheme by a factor of 9-12 without sacrificing discernible imaging details. Conclusion: Our proposed scheme significantly reduces the total acquisition time required for SRPT at a speed of one order of magnitude faster than the currently used scheme. This significant improvement in imaging speed would potentially promote the applicability of SRPT for imaging living organisms.