Density functional theory, Large unit cell, InN wurtzite nanocrystal. We have stimulated the electronic properties of wurtzite Indium Nitride by using density functional theory (DFT). The energy gap is size dependent at which E g increase with decreasing the size of InN nanocrystals. Also the lattice constant behaves in the same way as energy gap do. The cohesive energy is also calculated for the InN nanocrystals for 4, 8, 32 and 64 core atoms. Results shows that the cohesive energy values become larger as the size of core atoms increases and we predict that when we go for larger sizes the value of the cohesive energy will tend to be the same value of bulk InN.