We have investigated the composition and distribution of the wind of Sk 160, the supergiant companion of the X-ray star SMC X-1, by comparing an X-ray spectrum of the source, obtained with the ASCA observatory, during an eclipse with the computed spectra of reprocessed radiation from circumstellar matter with various density distributions. We show that the metal abundance in the wind of Sk 160 is no greater than a few tenths of solar, as has been determined for other objects in the Magellanic Clouds. We also show that the observed X-ray spectrum is not consistent with the density distributions of circumstellar matter of the spherically symmetric form derived for line-driven winds, nor with the density distribution derived from a hydrodynamic simulation of the X-ray perturbed and line-driven wind by Blondin & Woo (1995).