First-principles calculations of the structural, electronic and optical properties of ZnSnO3 were performed in the framework of density functional theory. The calculations indicate that the crystal structure of ZnSnO3 at ground state is LiNbO3 (LN)-type structure. The calculated band structure indicates that LN-type ZnSnO3 has a direct band gap of 2.42 eV. The analysis of partial density of states reveals that ZnSnO3 has a strong covalent feature. The dielectric function and refractive indices of ZnSnO3 are also calculated.