The amorphous titanium dioxide (a-TiO2) has drawn attention recently due to the finding that it holds promise for coating conventional photoelectrodes for corrosion protection while still allowing the holes to transport to the surface. The mechanism of hole conductivity at a level much higher than the edge of the valence band is still a mystery. In this work, an amorphous TiO2 model is obtained from molecular dynamics employing the "melt-and-quench" technique. The electronic properties, polaronic states and the hole conduction mechanism in amorphous structure were investigated by means of density functional theory with Hubbard's energy correction (DFT + U) and compared to those in crystalline (rutile) TiO2. The formation energy of the oxygen vacancy was found to reduce significantly (by a few eV) upon amorphization. Our theoretical study suggested that the oxygen vacancies and their defect states provide hopping channels, which are comparable to experimental observations and could be responsible for hole conduction in the "leaky" TiO2 recently discovered for the photochemical water-splitting applications.