Growth of Cr thin films on GaAs(001) was carried out using molecular beam epitaxy and was investigated by {\it in situ} reflection high energy electron diffraction (RHEED) and {\it ex situ} x-ray diffraction (XRD). The results show that there are two competing mechanisms during the growth, and the film structure strongly depends on the growth temperature. The single crystalline Cr films with the body-center-cubic (bcc) structure are succeeded, with the epitaxial relationship of (001)[001]_{Cr}//(001)[001]_{GaAs} and (001)[100]_{Cr}//(001)[100]_{GaAs}[pdf] [ postscript.gz]