An innovative Fourier Transform hyperspectral imaging system based on reflective optics is currently being studied. It can record both spatial images and spectral information of a sample instantaneously. Substantial properties of the sample can be elucidated from such images. Compared to classical Imaging Spectrometer using lenses and prisms, the significant characteristic of this system is that it only uses reflective mirrors and just one beam splitter. Such structure will help to largely avoid the limitation of spectral range and the refraction non-homogenize both of which affect the quality of imaging. Therefore, the noticeable advantages of this system are high signal-to-noise ratio, high spatial and spectral resolution, large spectral bandwidth, high throughput, non-chromatic aberration and very compact optical structure in which just one imaging system could applicable to a rather wide spectral bandwidth. This project includes both theoretical analysis and development of an experimental instrument. With the instrument, the images that contain one-dimensional spatial image and another dimensional interferogram are already collected. The data processing system could transform the interferogram of each scene to its spectral information. The typical experimental results are given in this paper.