A scheme of photoabsorption spectroscopy based on scanning tunneling microscopy (STM) has been developed by using a supercontinuum light as the wideband light source of a Fourier transform interferometer for spectroscopic measurements. The performance was demonstrated for a sample of GaAs. The proof-of-concept test showed that the use of the supercontinuum light instead of halogen lamps greatly enhances the signal-to-noise ratio due to the high brilliance of the supercontinuum light emitted from a small core of the photonic crystal fiber that enables tight focusing of the spectroscopy light onto the sample beneath the STM tip.