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We investigated the third-order optical nonlinearity of a new nonlinear optical crystal BaAlBO3F2 (BABF) using Z-scan technique with a picosecond 532-nm laser. Polarization-dependent nonlinear refractive index γ of the BABF crystal was measured with an a-cut sample and a sample cut along the type I phase-matching angle for third-harmonic-generation of lasers at 1064 nm (THG-cut). Anisotropy was observed with positive γ values in the range of 10-16 cm2/W, indicating self-focusing Kerr effects. The measurements agreed well with the theoretical prediction. The corresponding third-order nonlinear optical susceptibility χeff(3) was estimated to be ~ 10-14 esu.