Full polarization imaging plays an important role in remote sensing to distinguish artificial objects from the natural environment, recognizing objects in shadows and sun glint suppression. In this paper, we propose a broadband full Stokes channeled modulated polarization imaging system based on a Mach-Zehnder-grating interferometer (MZGI) with advantages such as compact size, low cost, snapshot ability, and high optical efficiency. It uses gratings to compensate for the dispersion of the carried frequency when inputting broadband light to generate interference fringes. Two detectors are assembled to the output plane to acquire the interference fringes. Each image obtained by the detectors can be individually demodulated into different Stokes parameters individually. When the two groups are combined together, the full Stokes parameters are obtained. The simulation and optical efficiency analysis demonstrate that the interference fringes can obtain the full polarization information simultaneously with high optical efficiency in broadband wavelengths.