We report on the structural characteristics and magnetic properties of Mn oxide films grown on MgO (001) substrates by plasma-assisted molecular beam epitaxy (MBE). Under well-controlled growth conditions, three types of Mn oxide films were obtained. They are Mn3O4, lambda -MnO2 and their mixed structure (Mn3O4 + lambda -MnO2). A structural phase diagram about the films is depicted as a function of growth rate and substrate temperature. It is found that at lower growth rate, a new phase of Mn oxide lambda -MnO2 was obtained, and two transition temperatures were observed in its magnetization. At a higher growth rate, the Mn3O4 film was obtained. Its coercive force and transition temperature were different from its bulk sample. The atomic force microscopy (AFM) images exhibited the surfaces of the three films are composed of pyramids, flat surfaces and truncated-pyramids, respectively.