To improve photoelectrochemical (PEC) activity of hematite, the modification of energy band by doping $3d$ transition metal ions Cu and Ti into $\alpha {\text{-Fe}}_2{\text{O}}_3$ were studied via the first-principles calculations with density function theory $\left(\text{DFT}\right)+U$ method. The results show that the band gap of hematite is $\sim 2.1\text{eV}$ and $n$ -type dopant Ti improves the electric conductivity, confirmed by recent experiments. The $p$ -type dopant Cu enhances the utilization ratio of solar energy, shifts both valance, and conduction band edges to a higher energy level, satisfying hydrogen production in the visible light driven PEC water splitting without voltage bias.