The greatest advantage of hyperspectral imaging technology over traditional detection technology is that it can record both spatial information and "fingerprint" spectral information of the observed target, with higher spectral resolution, higher detection capability, and can effectively identify and classify the target to be measured. With the development of hyperspectral imaging technology, the technology related to its core instrument, the Imaging Spectrometer, is also becoming more and more mature. Early developed Imaging Spectrometer are limited by the performance of spectroscopic devices, the band coverage is usually narrow. In order to achieve higher spectral coverage capabilities, multiple Imaging Spectrometer with completed stitching is usually needed, its volume and weight is large. Therefore, the study of a single broad-band spectral imaging system (0.4-1.7 μm) has important research significance. Grating has become the mainstream beam splitting element for broad-band spectral imaging systems because of its high dispersion capability and high environmental stability. The grating-based broad-band spectral imaging system suffers from the problem of crosstalk between multi-order diffraction spectra, which introduces serious stray light, which has a great impact on the performance of the optical system. Therefore, it is particularly important to carry out stray light analysis and suppression schemes for broad-band spectral imaging systems.Starting from a typical Schwarzschild structured grating-type broad-band spectral imaging system (Fig.1), the stray light of the optical machine system was analysed using the Monte Carlo non-sequential ray tracing method, Tracepro software was chosen to implement the simulation analysis of the broad-band spectral imaging system (Fig.3). The system stray light was evaluated based on the simulation analysis results (Fig.5), the theoretical calculation of the system stray light was carried out (Tab.3), and the theoretical calculation matched the simulation results. Secondly, based on the stray light path of the system obtained from the simulation, the source of multi-order stray light of the broad-band spectral imaging system was analysed in depth. A scheme of adding filters is proposed to suppress multi-level diffracted stray light. Two types of filters are designed: a sub-area filter (Fig.8) and a linear gradient bandpass filter (Fig.11), respectively.The stray light coefficient is significantly reduced after the addition of the sub-area filter, and the long-wave stray light is better suppressed with a maximum stray light coefficient of 0.011, but in the short-wave band, the stray light is still larger with a maximum stray light coefficient of 0.0826 (Fig.10). Therefore, the stray light in the long wavelength band can only be suppressed by using the sub-area filter, but the stray light in the short wavelength band is not effectively suppressed, which cannot meet the requirement of suppressing multi-order diffracted stray light in the broad-band imaging system. With the addition of a linearly graduated bandpass filter, stray light is not only suppressed at long wavelengths, but also at short wavelengths, and the stray light coefficient is reduced to the order of 10^-4 (Fig.14). Therefore, the use of a linear gradient bandpass filter for the suppression of stray light in a broad-band spectral imaging system can meet the requirements of the system. This paper analyzes the stray light problem of Schwarzschild structured planar grating type broad-band spectral imaging system. The analysis results show that there are two main types of stray light in broad-band spectral imaging system: one is the long wavelength multi-order diffracted light in the optical path multiple reflections and diffraction and short wavelength spectral channel overlap; the other is the short wavelength multi-order diffraction, adding linear gradient bandpass filter can effectively suppress the system multi-order diffracted stray light, which meets the requirements of broad-band spectral imaging system. The work of this paper provides a theoretical basis for the design of grating type broad-band spectral imaging system, and can be used for high-performance broad-band spectral imaging system.