We have performed a density functional calculation for the centrosymmetric neodymium gallate using a full-potential linear augmented plane wave method with the LDA and LDA+U exchange correlation. In particular, we explored the influence of U on the band dispersion and optical transitions. Our calculations show that U = 0.55 Ry gives the best agreement with our ellipsometry data taken in the VUV spectral range with a synchrotron source. Our LDA+U (U = 0.55) calculation shows that the valence band maximum (VBM) is located at T and the conduction band minimum (CBM) is located at the center of the Brillouin zone, resulting in a wide indirect energy band gap of about 3.8 eV in excellent agreement with our experiment. The partial density of states show that the upper valence band originates predominantly from Nd-f and O-p states, with a small admixture of Nd-s/p and Ga-p B-p states, while the lower conduction band prevailingly originates from the Nd-f and Nd-d terms with a small contribution of O-p-Ga-s/p states. The Nd-f states in the upper valence band and lower conduction band have a significant influence on the energy band gap dispersion which is illustrated by our calculations. The calculated frequency dependent optical properties show a small positive uniaxial anisotropy.