The surface morphology of epitaxial Fe(001)/MgO(001)/Fe(001) magnetic tunnel junctions, which show the giant tunneling magnetoresistance effect, was investigated by in situ scanning tunneling microscopy. It was observed that an epitaxial MgO barrier layer forms flat surface structures. The surface was flatter with distinct steps and terraces after annealing, which would lead to an increase of the tunneling magnetoresistance ratio. Examination of the local electronic structures of 1.05-nm-thick MgO barrier layers by scanning tunneling spectroscopy revealed no pinholes in the layers, so they would be perfect barriers in magnetic tunnel junctions.