Using computer-controlled pulsed laser deposition, high quality SrMoO3 thin films have been epitaxially grown on SrTiO3 (001) substrates. A growth interruption technique was employed for better epitaxy, and layer-by-layer growth was obtained by the intensity oscillations of reflection high-energy electron diffraction. The films were of epitaxial crystallinity as characterized by high-resolution transmission electron microscopy. The typical root mean square surface roughness was 2.2 Angstrom. The SrMoO3 thin films showed metal-like conducting behavior with resistivity on the order of 60-120 mu Omega cm between 4 K and room temperature. An x-ray photoelectron spectroscopy study shows that the valence band spectrum of the film has the typical character of a metal, and Mo 4dt(2g) electrons an responsible fur the conduction of the films.