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In this paper, we investigate the electronic and optical properties of MgO nanosheet in (100) and (111) directions. Our calculations carried out under the framework of density functional theory (DFT) exploiting WIEN2K code with Full potential, periodic boundary conditions, augmented plane-wave basis sets and GGA approximation. Electronic results indicate that MgO(111) nanosheet has an indirect band gap of 3.67 eV and MgO(100) nanosheet has a direct band gap of 3.14 eV. MgO(100) nanosheet exhibit more ionic bonding than MgO(111) and MgO(111) has more covalent bonding than MgO(100) nanosheet. Moreover, the optical results indicate that variation of dielectric function in x direction is more than the z direction. DOS and imaginary part of the dielectric function survey confirm semiconductor properties with different bang gap for structures. Comparing the imaginary part of dielectric functions in x and z directions for two structures, blue and red shift have been observed respectively. Our results indicate that these two nanostructures are transparent in a wide range of energy spectra and have low reflectivity. [ABSTRACT FROM AUTHOR]