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Stimulated Raman projection tomography is a label-free volumetric chemical imaging technology allowing three-dimensional (3D) reconstruction of chemical distribution in a biological sample from the angle-dependent stimulated Raman scattering projection images. However, the projection image acquisition process requires rotating the sample contained in a capillary glass held by a complicated sample rotation stage, limiting the volumetric imaging speed, and inhibiting the study of living samples. Here, we report a tilt-angle stimulated Raman projection tomography (TSPRT) system which acquires angle-dependent projection images by utilizing tilt-angle beams to image the sample from different azimuth angles sequentially. The TSRPT system, which is free of sample rotation, enables rapid scanning of different views by a tailor-designed four-galvo-mirror scanning system. We present the design of the optical system, the theory, and calibration procedure for chemical tomographic reconstruction. 3D vibrational images of polystyrene beads and C. elegans are demonstrated in the C-H vibrational region.