The structural and magnetic properties of the epitaxial (0 0 1) SrMnO3 (SMO) thin film grown on (0 0 1) SrTiO3 (STO) substrate by molecular beam epitaxy (MBE) are reported. In-situ reflection high energy electron diffraction (RHEED) intensity oscillation is utilized to precisely adjust the stoichiometry by tuning the atom source shuttered time during the growth. The surface of the thin film with obvious steps and terraces is observed to be atomically flat. The epitaxial single crystal SMO thin film which is grown along the direction of (0 0 1) STO substrate is confirmed to be four-fold symmetric along the (0 0 1) azimuth by X-ray diffraction phi scan. The XRD reciprocal space map indicates that the SMO thin film is effectively strained in the present thickness and is typical tetragonal crystal structure. It is found that the present SMO thin film is ferromagnetic. The factors, namely Mn3+-Mn4+ double exchange coupling, oxygen vacancies and the strain, lead the SMO thin films to produce ferromagnetism.