Electronic structures, dielectric functions, refraction indices, absorption spectra of perfect YTaO4 and LuTaO4 crystals are calculated using pseudo-potentials and plane waves based on first-principles method. The results show that valence bands of YTaO4 and LuTaO4 are both from O2p states. Conduction band is divided into two parts. The lower conduction band is mainly composed of Ta5d states and the upper conduction band involves contribution mainly from Y4d states of YTaO4 and Lu5d states of LuTaO4. When ω equals to zero, the dielectric constants and refractive indices between YTaO4 and LuTaO4 are close to each other. The low-energy characteristic peaks below 10.0 eV of their imaginary parts originate from the electron transition within TaO3-4 complex. The low-energy characteristic peaks between 10.0 eV and 15.0 eV correspond to the electron transition from valence band to the upper conduction band. The peaks beyond 15.0 eV are due to the electron transition from O2s to conduction band. Last but not the least, the ultraviolet absorption bands of YTaO4 and LuTaO4 are broad and strong. They correspond to the charge transfer transition from oxygen (2p) to d0 ion of tantalum.