Nanoporous titanium dioxide ($TiO_2$) is very attractive material for various applications due to the high surface to volume ratio. In this study, we have fabricated nanoporous $TiO_2$ thin films on Si by anodic oxidation. 500-nm-thick titanium (Ti) films were deposited on Si by using electron beam evaporation. Nanoporous structures in the Ti films were obtained by anodic oxidization using ethylene glycol electrolytes containing 0.3 wt% $NH_4F$ and 2 vol% $H_2O$ under an applied bias of 5 V. The diameter of nanopores in the Ti films linearly increased with anodization time and the whole Ti layer could become nanoporous after anodizing for 3 hours, resulting in vertically aligned nanotubes with the length of 200~300 nm and the diameter of 50~80 nm. Upon annealing at $600^{circ}C$ in air, the anodized Ti films were fully crystallized to $TiO_2$ of rutile and anatase phases. We believe that our method to fabricate nanoporous $TiO_2$ films on Si is promising for applications to thin-film gas sensors and thin-film photovoltaics.