By using in-situ reflection high energy electron diffraction, the epitaxial growth of Co films on GaAs(001) surface is studied. When the growth temperature was 150℃, the growth process of Co films can be divided into three stages. The crystal structure of the first 3nm of the Co film is body-center-cubic(bcc) metastable phase. Then the next 4nm film is a complicated polycrystalline phase. After the thickness exceeds 7nm, the Co film is a single-crystalline hexagonal-close-packed(hcp) stable phase. This new result clears up the controversy in former experiments about the structure of the Co epilayer, and establishes, for the first time to our knowledge, a clear physical picture of the epitaxial growth of Co films on GaAs(001).