The nonlinear optical properties of some ABO3 materials (BaTiO3, KNbO3, LiTaO3 and LiNbO3) are studied by density functional theory (DFT) in the local density approximation (LDA) expressions based on first-principle calculations. Our goals are to give the details of the calculations for linear and nonlinear optical properties, including the linear electro-optic (EO) tensor for some ABO3 structures with oxygen octahedral structures using first-principles methods. These results can then be used in the study of the physics of ferroelectrics, specifically, we present calculations of the second harmonic generation response coefficient X
ijk(2) (−2ω, ω, ω) over a large frequency range for ABO3 crystals. The electronic linear EO susceptibility X
ijk(2) (−ω, ω,0) is also evaluated below the band gap. These results are based on a series of the LDA calculations using DFT. Results for X
ijk(2) (−ω, ω,0) are in agreement with experiments below the band gap. The results are compared with the theoretical calculations and the available experimental data.