A spectral imaging system consisting of a Fourier transform-infrared spectrometer, a high-speed infrared camera, and a bundle of hollow-optical fibers transmitting infrared radiation images was constructed. Infrared transmission spectra were obtained by carefully processing multiple interferograms taken by high-speed photography. Infrared spectral images of a variety of samples captured by the system were measured. We successfully detected existence maps of the oil and fat of biological samples by mapping the transmission of specific wavelengths in the spectrum.