Channeled modulated polarimetry imaging (CMPI) is a novel detection technology which can acquire full-Stokes parameters of each pixel of the sensor. Compared with the other imaging polarimetric technologies, CMPI has advantages in compact, high spatial resolution and acquiring full-Stokes information simultaneously. It has been widely used in remote sensing, military reconnaissance and biomedical diagnosis. However CMPI can only be used for quasi-monochromatic light during full-Stokes imaging, which leads to low signal-to-noise ratio in many cases especially under the condition of low light. Expanding the imaging spectral bandwidth of the CMPI is of great urgency. In order to expand the bandwidth, the limitation factors and conditions of the imaging bandwidth should be clearly understood first. So an imaging bandwidth criterion is deduced in this paper for the researchers to estimate the limitation bandwidth of the CMPI. We analyze the factors which might affect the fringe visibility based on a Savart plate (SP) CMPI and obtain the conclusion that carry frequency (CF) is the main factor which restricts the bandwidth. Then, according to the definition of CF, = /(f), in which is the shearing distance of SP, is the imaging wavelength, and f the focal length of imaging lens, we investigate how these factors influence the CF. It turns out that is the main factor which causes the fringe to arise in a certain CPI system while would add an error to CF within 5% in visible light domain. To investigate how the wavelength influences the imaging spectral bandwidth, we deduce the total irradiance on the image plane under broadband light and use Fourier transform for it to obtain the distribution of the spatial frequency of the image plane. And the conclusion is obtained that the CF bandwidth be expressed as (20-1/(2L), 20 + 1/(2L)) referred to as the Rayleigh criterion, in which 0 is the central CF and L is the range of the imaging plane. After substituting the relevant parameters into the CF bandwidth, we can obtain the imaging spectral bandwidth criterion equation as = 2D02/(4D2-02) , in which is the maximum imaging bandwidth, D is the maximum optical path difference, and 0 is the central wavelength of the CMPI system. To validate the accuracy of the spectral bandwidth criterion, some simulations are conducted to generate a maximum imaging spectral bandwidth while the visibility of the fringes decreases to 0.5 for the fringes which cannot be distinguished when the visibility is less than 0.5. The results show that the error between the simulated spectral bandwidth and the calculated spectral bandwidth is less than 1 nm. This criterion value fits the test well for the SP CMPI system. In addition, it can also be used for estimating the maximum imaging bandwidth of the other CMPI system whose shearing distance is independent or quasi-independent of wavelength.