Magnesium ferrite is a very important magnetic material due to its interesting magnetic and electrical properties and its chemical and thermal stability. Here we report on the magnetic and transport properties of epitaxial MgFe2O4 thin films grown on MgO (001) by molecular beam epitaxy. The structural properties and chemical composition of the MgFe2O4 films were characterized by X-Ray diffraction and X-Ray photoelectron spectroscopy, respectively. The nonsaturation of the magnetization in high magnetic fields observed for M (H) measurements and the linear negative magnetoresistance (MR) curves indicate the presence of anti-phase boundaries (APBs) in MgFe2O4. The presence of APBs was confirmed by transmission electron microscopy. Moreover, post annealing decreases the resistance and enhances the MR of the film, suggesting migration of the APBs. Our results may be valuable for the application of MgFe2O4 in spintronics.