The ASCA SIS and ROSAT PSPC spectral data of the supernova remnant 3C 397 are analyzed with a two-component nonequilibrium ionization model. In addition, the ASCA SIS0 and SIS1 spectra are fitted simultaneously in an equilibrium case. The resulting values of the hydrogen column density yield a distance of similar to 8 kpc to. 3C 397. It is found that the hard X-ray emission, containing S and Fe K alpha lines, arises primarily from the hot component, while most of the soft emission, composed mainly of Mg, Si, and Fe L lines and continuum, is produced by the cool component. The emission measures suggest that the remnant evolves in a cloudy medium and imply that the supernova progenitor might not be a massive early-type star. The cool component is approaching ionization equilibrium. The ages estimated from the ionization parameters and dynamics are all much greater than the previous determination. We restore the X-ray maps using the ASCA SIS data and compare them with the ROSAT HRI and the NRAO VLA Sky Survey 20 cm maps. The morphology with two bright concentrations suggests a bipolar remnant encountering a denser medium in the west.