The band structures and the densities of states at the Fermi energy for rutile, anatase and brookite phases are investigated along with the structure-photocatlaytic relationship by using DFT method. Bands are less dispersive in anatase phase than in rutile phase, and they are almost flat in brookite phase. As a result, the DOS value near the Fermi energy for brookite is highest among three types of $TiO_{2}$, which means that the numbers of electrons near the Fermi energy are largest in brookite. The calculation shows that brookite phase may exhibit highest photocatalytic efficiency among three types of $TiO_{2}$.