Epitaxial thin films of a half-metallic ferromagnet Sr2FeMoO6 have been grown on (001) SrTiO3, and MgO substrates by magnetron sputtering in Ar+H2 mixture gas. Their structural, magnetic, magneto-optical and transport properties at room temperature were investigated and compared. Large difference has been observed especially in the magnetic and magneto-optical properties between thin films on SrTiO3 and MgO. The films on SrTiO3 exhibited stronger out-of-plane magnetic anisotropy and larger complex polar Kerr effect with a rotation θk up to -0.32° at 1.6 eV and RT. The observed difference in the properties of the films on the two substrates can be interpreted in terms of the structural disorder.