Based on density functional theory (DFT), the effects of scandium (Sc) doping and oxygen vacancy (VO) on the electronic states and optical properties of BiVO4 are investigated. GGA+U method is adopt during the calculation of the electronic properties to compensate the limitation of DFT method. The ideal BiVO4 has a direct band gap of 2.400 eV, and if Bi in BiVO4 is substituted by Sc (sub Sc-Bi), the direct band gap will be reduced to 2.393 eV. However, if V is replaced by Sc (sub Sc-V) as well as that with oxygen vacancy induced (sub Sc-V+Vo), the band gap will become indirect one with values of 1.913 eV and 2.198 eV, respectively. The reduction capability is in the sequence of sub Sc-Bi > ideal > sub Sc-V+Vo > sub Sc-V, while the oxidation capability is in the order of ideal > sub Sc-Bi > sub Sc-V+Vo > sub Sc-V. The ε<sub>1</sub> (0) of the ideal, sub Sc-Bi, subSc-V and sub Sc-V+Vo defective BiVO4 is 8.290, 8.293, 12.791 and 8.285, respectively. The optical absorptions of ideal and sub Sc-Bi BiVO4 show anisotropy and they are nearly independent on the defect concentration. Sub Sc-V BiVO4 exhibits stronger absorption than the other three semiconductors. The absorptions of sub Sc-V+Vo BiVO4 vary obviously with the defect concentrations, where 3.906% defect concentration of BiVO4 has the strongest absorptions. The estimated optical band gaps are smaller than for ideal and defective BiVO4.