The electronic structure of zinc blend indium gallium phosphide In0.5Ga0.5P nanocrystals which have dimension (2-2.8 nm) is investigated using the density functional theory coupled with large unit cell (LUC) for the different size core (8 ,16,54,64) atoms respectively. The investigated properties include total energy, energy gap, conduction band, valence band, cohesive energy, ionicity and density of state etc. as a function of core size and lattice constant. Results show the shape effect of increasing the core size and lattice constant on these electronic properties