We have performed Cr and Co K-edge x-ray-absorption measurements to investigate the dependence of local electronic and atomic structures on the Cr-layer thickness in epitaxial Co (40A)/Ct (t~) (t~ = 2, 3, 5, 7, and 9A) multilayers. The Cr K x-ray absorption near edge structure (XANES) spectra of Co/Cr multilayers indicate an abrupt transition of the Cr layer from a bcc structure to a hcp structure when the thickness of the Cr layer is decreased down to -5A or three atomic layers. The structural transition and bond-length distortion in Cr and Co layers observed in the extended x-ray absorption fine structure (EXAFS) measurements are consistent with the XANES results.