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The basic principle of channeled Fourier-transform imaging spectropolarimeter (CFTISP) is outlined. The two mainstream techniques existing for performing polarization state demodulation are analyzed, which show uncertainty that may not be suitable for CFTISP based on lateral shear interferometer. A modified demodulation method for Stokes parameters is described. The method separate the phase of the sign and the high-order retarders’ retardations from the total phase acquired from the fast Fourier transform of the interferogram, which will not cause the amplitude error from the reference beam. Furthermore, the retardations and the residual phase error in each band introduced by instrument can be seen directly in this method. The effectiveness of this method is experimentally demonstrated with four known input states of polarization, and the results are satisfactory. The RMS error of each Stokes parameters is also presented, which demonstrates that the low spectral signal-to-noise ratio can increase the RMS error by nearly a factor of 2–5 for the individual Stokes parameters. The comparison of reconstructed results by four methods further demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]