This paper presents a snapshot spectroscopic Mueller matrix polarimetry based on spectral modulation. The polarization state generator consists of a linear polarizer in front of two high-order retarders, and the polarization state analyzer is formed by two non-polarization beam splitters incorporated with three high-order retarder/linear analyzer pairs. It can simultaneously generate three modulated spectra used for reconstructing the 16 spectroscopic Mueller elements of the sample. Since each of the modulated spectra produces seven separate channels equally spaced in the Fourier domain, the channel bandwidth can be enhanced efficiently compared with the conventional spectrally modulated spectroscopic Mueller matrix polarimetry. The feasibility of the proposed spectroscopic Mueller matrix polarimetry is demonstrated by the experimental measurement of an achromatic quarter-wave plate. © 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.