Thin layers of the body-centered-cubic (bcc) cobalt (Co) phase with (001) orientation have been grown on single-crystalline Fe(001). Reflection high-energy electron diffraction (RHEED) and x-ray diffraction (XRD) have been used to investigate the surface and the bulk crystal structure of the deposited Co films. The RHEED investigation shows that the bcc Co structure can be stabilized up to about 8 atomic monolayers (at. ML) and that the bcc Co surface is more atomically rough as compared to Fe but improves with increased growth temperature. RHEED patterns from thicker Co films indicate a transformation from the bcc structure to a hexagonal close packed (hcp). The XRD investigation shows that this hcp phase is textured and that the films contain a small amount of Co with a face-centered-cubic stacking sequence.