A Fourier-transform imaging spectropolarimeter is presented and demonstrated. It is composed of a time-division polarization modulator and a high radiation throughput Fourier-transform spectrometer. Four polarization states of the input light are generated by rotating the retarder. Then, the polarized light enters the Fourier-transform spectrometer to create four sets of interferometric images, where we can recover four polarization spectra and calculate the full-Stokes vector in various wavenumber frequency. The method has good performance to resist instrument noise and has the advantage of high spatial resolution. The laboratory setup is described and the noise source is analyzed. Two proven experiments have been carried out in visible light.