We report, for the first time, the characterizations on optical nonlinearities of beta-phase gallium oxide (beta-Ga2O3), where both (010) beta-Ga2O3 and ((2) over bar 01) beta-Ga2O3 were examined for two-photon absorption coefficient, Kerr nonlinear refractive index, and their polarization dependence. The wavelength dependence of two-photo absorption coefficient and Kerr nonlinear refractive index were also estimated by a widely used analytical model. beta-Ga2O3 exhibits a two photon absorption (TPA) coefficient of 1.2 cm/GW for (010) beta-Ga2O3 and 0.6 cm/GW for ((2) over bar 01) beta-Ga2O3. The Kerr nonlinear refractive index is -2.1 x 10-15 cm(2)/W for (010) beta-Ga2O3 and -2.9 x 10(-15) cm(2)/W for ((2) over bar 01) beta-Ga2O3. In addition, beta-Ga2O3 shows stronger in-plane nonlinear optical anisotropy on ((2) over bar 01) plane than on (010) plane. Compared with GaN, TPA coefficient of beta-Ga2O3 is 20 times smaller, and the Kerr nonlinear refractive index of beta-Ga2O3 is also found to be 4-5 times smaller. These results indicate that beta-Ga2O3 have the potential for ultra-low loss waveguides and ultra-stable resonators and integrated photonics, especially in UV and visible wavelength spectral range. (C) 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement