The structural and electronic properties of yttrium tantalate (YTaO4) and yttrium niobate (YNbO4) crystals are studied using experimental and first-principles GGA U total energy calculations. The band gap of the host lattice from absorption and luminescence experiment is measured to be 5.1 eV for YTaO4 and 4.1eV for YNbO4. This is close to 5.14 eV and 4.28 eV, respectively, reproduced by means of GGA U approach. In our calculation, we tune both Hubbard energy U and exchange parameter J to reproduce the energy gap measured experimentally. It is found that Hubbard energy U plays a major role in reproducing the experimentally measured energy gap, but exchange parameter J does not. We also calculate the density of states (DOS) using the optimized U to interpret the experimentally measured luminescence spectra. Both the experimental and DOS calculations show that the valence band of tantalate (Ta) and niobate (Nb) systems is mainly composed of oxygen (O) 2p states. The lower conduction band is mainly composed of Ta 5d states or Nb 4d states, respectively, while the upper conduction band involves the contribution mainly from yttrium (Y) 4d states, with the middle conduction band mainly a mixture of Ta or Nb and Y states. The calculated partial DOS of each atom in the tantalate and niobate system is then compared with the UV and VUV spectra from photoluminescence excitation (PLE) experiment to explain the nature of the bands observed.