We present experimental results of birefringence property measurements for two types of negative curvature anti-resonant hollow-core fibers (AR-HCFs). Both AR-HCFs have a core of 50 µm in diameter, providing an effective area of the fundamental guided mode larger than 1000µm2. Measurements were carried out at wavelengths of 2.25, 2.35, and 2.45 µm. The obtained results demonstrate that both fiber types have birefringence axes that do not correspond to core symmetry axes. The proposed technique for the birefringence axes orientation measurement could be applied to other kinds of HCFs at various wavelengths.