A hyperspectral Mueller matrix imaging (HMMI) method to capture spatial, spectral and Mueller matrix images at the same time is proposed. The principle of hyperspectral Mueller matrix imaging and the shear interference imaging process of birefringent interferometer are discussed in detail. The joint optimization design of polarization state generator and polarization state analyzer as well as the calibration method of this system is shown. In order to verify the performance of the instrument, the spectral Mueller matrix imaging of the target in the laboratory proves the feasibility of HMMI in quickly acquiring spectral images and Mueller matrix images. Because of its high spectral resolution and fast polarization modulation, it provides a new idea for the development of spectral Mueller matrix imaging.