With the help of ab initio full-potential linearized augmented plane wave method, the calculations of the electronic structure and linear optical properties are carried out for CaCO3. It is found that the CaCO3 compound has a direct band gap of 4.29119 eV. The hybridization of C atomic 2s and O atomic 2s orbitals forms the anion groups ［CO3］2-. Furthermore, the different origin of the mean peaks of imaginary part of dielectric function of CaCO3 has been discussed. The absorption coefficient, electron energy loss coefficient, refractive index, and extinction coefficient of CaCO3 are studied.