A kind of air- core photonic band gap fiber (PBF) with outstanding polarization- maintaining (PM) property is proposed. The effects of temperature variation on the effective index, beat-length and confinement loss are studied numerically based on full vector finite element method (FEM). It is found that the birefringence of the PBF is as high as 6.19×10^-3, and beat-length is as short as 0.25 mm at the wavelength of 1.55 μm. The beat-length of this PBF is insensitive to the temperature, and the temperature-dependent beat-length coefficient is as low as 2.86×10^-8 m/℃, which is typically two orders of magnitude lower than those of conventional panda fibers. The loss of the PBF is sensitive to temperature, and the confinement loss of the two orthogonal polarized modes increase with the increasing temperature. The PM-PBF with ultra-low temperature-dependent beat-length coefficient can reduce errors induced by the thermally polarization crosstalk apparently in interferometric applications such as resonant fiber optic gyroscope (RFOG), which plays an important role in RFOG, optical communications, optical fiber sensors and so on.