The　electronic　structure,　carrier　transport　and　the　optical　absorption　proprerties　of　the　Na　doped　TiO　2　have　been　studied　by　the　pseudo-potential　density　functional　theory　method.　The　pure　TiO　2　has　direct　band　gap　of　2.438　eV　and　the　Na　doped　TiO　2　exibits　decreased　band　gap　value　of　1.976　eV.　The　pure　TiO　2　has　five　bands　while　the　Na　doped　TiO　2　has　seven　bands.　The　TiO　2　has　higher　carrier　mobility　than　that　of　the　Na　doped　TiO　2　,　however　the　Na　doped　TiO　2　has　heavier　carrier　effective　mass　than　that　of　the　TiO　2　.　The　dopant　Na　has　induced　hole　carriers　and　new　bands　in　to　the　valance　bands.　The　Na　doping　increases　the　carrier　concentration　of　the　TiO　2　,　the　Ti　p　electrons,　Na　p　electrons　and　the　O　p　electrons　play　importan　role　in　the　carrier　conduction　process.　The　optical　absorption　region　has　been　expanded　to　low　energy　range.　©　2018,　Chinese　Ceramic　Society.　All　right　reserved.