We report, for the first time, the characterizations on optical nonlinearities of beta-phase gallium oxide (β-Ga2O3), where both (010) β-Ga2O3 and (2¯01) β-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. β-Ga2O3 exhibits a two photon absorption (TPA) coefficient of 1.2 cm/GW for (010) β-Ga2O3 and 0.6 cm/GW for (2¯01) β-Ga2O3. The Kerr nonlinear refractive index is -2.1 × 10-15 cm2/W for (010) β-Ga2O3 and -2.9 × 10-15 cm2/W for (2¯01) β-Ga2O3. In addition, β-Ga2O3 shows stronger in-plane nonlinear optical anisotropy on (2¯01) plane than on (010) plane. Compared with GaN, TPA coefficient of β-Ga2O3 is 20 times smaller, and the Kerr nonlinear refractive index of β-Ga2O3 is also found to be 4-5 times smaller. These results indicate that β-Ga2O3 have the potential for ultra-low loss waveguides and ultra-stable resonators and integrated photonics, especially in UV and visible wavelength spectral range.