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We report the successful growth of the tetragonal FeS film with one or two unit-cell (UC) thickness on SrTiO3 (001)substrates by molecular beam epitaxy.Large lattice constant mismatch with the substrate leads to high density of defects in single-UC FeS,while it has been significantly reduced in the double-UC thick film due to the lattice relaxation.The scanning tunneling spectra on the surface of the FeS thin film reveal the electronic doping effect of single-UC FeS from the substrate.In addition,at the Fermi level,the energy gaps of approximately 1.5 meV are observed in the films of both thicknesses at 4.6K and below.The absence of coherence peaks of gap spectra may be related to the preformed Cooper-pairs without phase coherence.