Herein, a spatially modulated snapshot computed tomographic polarization imaging spectrometer (SMSCTPIS) is proposed. This instrument can obtain spatial, intensity, and polarization information of different wavelengths of a target simultaneously. It can also alleviate certain limitations of the spatially modulated snapshot imaging polarimeter (SMSIP) based on a Savart polarizer, which cannot obtain information of different wavelengths in a single measurement. Further, it can also mitigate the need to frequently replace the filters of SMSIPs for different detection wavelengths. The paper introduces the structure and principle of the SMCTPIS first, followed by experiments confirming its accuracy. Finally, the experimental results are analyzed, and conclusions are drawn.