We developed a compact synchrotron X-ray topography system equipped with a demountable Si channel-cut crystal monochromator with an energy range of 5-20 keV at beamline 09A in SAGA Light Source (SAGA-LS) to enable switching between a white X-ray beam and a monochromatic X-ray beam. The position of incidence of the X-ray beam on the sample is kept constant because the beam-path difference, which is caused by inserting the monochromator and by tuning the X-ray energy, is adjusted automatically. Two possible applications of this system are proposed: (1) the observation of dislocations in a thick Si rod by white X-ray topography, and (2) a comparative study of X-ray images of defects and strain in a 4H-SiC wafer captured using white and monochromatic X-ray beams.