Thin Fe3O4 (110) films, grown by molecular-beam epitaxy on MgO, have been studied by scanning tunneling microscopy and spectroscopy. A 500-Angstrom-thick film was cleaned prior to the measurements by annealing at 850 K under ultrahigh vacuum. Tunneling images show the onset of the formation of the one-dimensional row reconstruction, which was previously also observed on surfaces of bulk single crystals cleaned by ion bombardment and subsequent annealing. Spectroscopic current-voltage curves reveal different behavior depending on the location of the tip above the row reconstruction. Most notably, when probing the filled states at negative sample bias, a larger current was found on top of the rows as compared to a tip position between two rows.