A cobalt oxide - tin oxide nanocomposite based gas sensor on an $SiO_2$ substrate was fabricated. Granular thin film of tin oxide was formed by a rheotaxial growth and thermal oxidation method using dc magnetron sputtering of Sn. Nano particles of cobalt oxide were spin-coated on the tin oxide. The cobalt oxide nanoparticles were synthesized by polymer-assisted deposition method, which is a simple cost-effective versatile synthesis method for various metal oxides. The thickness of the film can be controlled over a wide range of thicknesses. The composite structures thus formed were characterized in terms of morphology and gas sensing properties for reduction gas of $H_2$. The composites showed a highest response of 240% at $250^{circ}C$ upon exposure to 4% $H_2$. This response is higher than those observed in pure $SnO_2$ (90%) and $Co_3O_4$ (70%) thin films. The improved response with the composite structure may be related to the additional formation of electrically active defects at the interfaces. The composite sensor shows a very fast response and good reproducibility.