This paper proposes a spatial heterodyne Raman spectrometer (SHRS) based on a multi-Littrow-angle multi-grating (MLAMG). Compared with a conventional multi-grating, the MLAMG not only provides higher spectral resolution and a broader spectral range, but is also easier to produce. A verification breadboard system is built using the MLAMG combined with four sub-gratings with a groove density of 300 gr/mm and Littrow angles of 4.6355°, 4.8536°, 5.0820°, and 5.3253°. This MLAMG-SHRS is used to obtain the Raman spectra of inorganic solids and organic solutions for different integration times, laser powers, suspension contents, and containers. The Raman spectra of mixed targets and minerals are also presented. The experiments demonstrate that the MLAMG-SHRS is suitable for broadband measurements at high spectral resolution in a wide range of potential applications.