An optical system of reflective static Fourier transform spectrometer is designed based on the double right-angle beam splitter, and the prototype is built. The light splitting device of the spectrometer optical system adopts double right-angle beam splitter, and the other optical paths adopt the reflective structure to fold the optical path effectively. Compared with the transmission-type static Fourier spectrometer, the volume of the system is reduced by more than half. The peak spectrum lines of 404.7,435.8,546.1, 577.0 nm are obtained by using mercury lamp as the light source of static Fourier spectrometer. The result shows that the actual spectrum of the mercury lamp is well reconstructed. The experimental results show that the spectral resolution is about 5.93 nm at the laser wavelength of 650 nm, which is consistent well with the result of theoretical calculation. The optical system has many advantages, such as compact structure, small size, light weight, strong seismic resistance, etc. It can provide the technical support for the development of miniaturized and portable static Fourier spectrometer.