Polycrystalline powder of trigonal BaZnO2 has been synthesized and characterized by X-ray diffraction, dielectric measurements, and vibrational spectroscopy (infrared and Raman). These properties have been also calculated using the density functional theory and compared with the experimental ones. The experimental phonon modes have been assigned, and we have revisited the previous theoretical assignment reported in the literature combining the calculated and the experimental data. The dielectric constant has been analyzed by decoupling it into three contributions (electronic, phonon, and strain). The second-order nonlinear susceptibility and the electro-optic response have been predicted as no theoretical or experimental investigations of these optical properties have been previously reported in the literature. The second-order nonlinear optical susceptibility and the electro-optic coefficients of BaZnO2 are predicted to be significantly higher than those reported in α-quartz or α-GeO2. Thus, considering the stability of BaZnO2 within a large range of temperature, this compound could be a possible candidate for nonlinear optical applications when compared with α-quartz.