We carried out ab initio calculations of structural, electronic and optical properties of Indium nitride ( InN ) compound in both zinc blende and wurtzite phases, using the full-potential linearized augmented plane wave method (FP-LAPW), within the framework of density functional theory (DFT). For the exchange and correlation potential, local density approximation (LDA) and generalized gradient approximation (GGA) were used. Moreover, the alternative form of GGA proposed by Engel and Vosko (EV-GGA) and modified Becke–Johnson schemes (mBJ) were also applied for band structure calculations. Ground state properties such as lattice parameter, bulk modulus and its pressure derivative are calculated. Results obtained for band structure of these compounds have been compared with experimental results as well as other first principle computations. Our results show good agreement with the available data. The calculated band structure shows a direct band gap Γ → Γ. In the optical properties section, several optical quantities are investigated; in particular we have deduced the interband transitions from the imaginary part of the dielectric function.