Structural, elastic, mechanical, electronic properties, and dispersion of optical functions of hexagonal ZnTiO3 have been investigated from first-principles within density-functional theory (DFT) using the norm-conserving pseudopotentials method, within the generalized gradient approximation (GGA) to the exchange-correlation functional. The calculated structural parameters agree with the available experimental and theoretical results. The elastic constants, bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and Lamé's constants as well as mechanical stability have been studied, indicating that hexagonal ZnTiO3 is mechanically stable, anisotropic, and ductile. The electronic structure and chemical bonding of hexagonal ZnTiO3 have been analyzed according to the calculated energy band structure, density of states (DOS), and charge populations. Dispersion of optical functions is shown and analyzed, including the complex dielectric function, refractive index, extinction coefficient, reflectivity, absorption coefficient, loss function, and optical conductivity.