This paper presents a multi-grating-based cross-dispersed spatial heterodyne spectrometer (MGCDSHS). The principle of generation of two-dimensional interferograms for two cases, where the light beam is diffracted by one sub-grating or two sub-gratings, is given and equations for the interferogram parameters in these two cases are derived. An instrument design with numerical simulations is presented that demonstrates the spectrometer's ability to simultaneously record separate interferograms corresponding to different spectral features with high resolution over a broad spectral range. The design solves the mutual interference problem caused by overlapping of the interferograms, and also provides the high spectral resolution and broad spectral measurement range that cannot be achieved using conventional SHSs. Additionally, by introducing cylindrical lens groups, the MGCDSHS solves the throughput loss and light intensity reduction problems caused by direct use of multi-gratings. The MGCDSHS is compact, highly stable, and high-throughput. These advantages make the MGCDSHS suitable for high-sensitivity, high-resolution, and broadband spectral measurements.