A hollow-core fiber using anisotropic anti-resonant tubes in thecladding is proposed for low loss and effectively single-mode guidance. We show that the loss performance and higher-order mode suppression is significantly improved by using symmetrically distributed anisotropic antiresonant tubes in the cladding, elongated in the radial direction, when compared to using isotropic, i.e. circular, anti-resonant tubes. The effective single-mode guidance of the proposed fiber is achieved by enhancing the coupling between the cladding modes and higher-order-core modes by suitably engineering the anisotropic anti-resonant elements. With a silicabased fiber design aimed at 1.06 µm, we show that the loss extinction ratio between the higher-order core modes and the fundamental core mode can be more than 1000 in the range 1.0-1.65 µm, while the leakage loss of the fundamental core mode is below 15 dB/km in the same range.