Modern optical networks require broadband, high-speed, large-capacity transmission techniques. Based on the anti-resonant reflecting optical waveguiding mechanism, we propose a polarization-maintaining (PM) hollow-core optical fiber. The light is confined by four tubes, which have different thicknesses along two orthogonal directions to achieve efficient PM guidance. To enhance the PM performance while achieving low propagation loss, we investigate the effects of additional anti-resonant layers in the tubes, tube thickness, air-core size and the distance between two adjacent tubes. Numerical simulations indicate that, at 1550 nm, the proposed fiber supports two orthogonally polarized modes with the birefringence of 1.2×10^-4 and the propagation losses of HE_11x and HE_11y modes are 0.002 dB/m and 0.013 dB/m respectively. Moreover, within 1425~1725 nm (bandwidth of 300 nm), the birefringence of the proposed fiber is no less than 1.0×10^-4, the propagation losses are within 0.002 dB/m and 0.185 dB/m, and the dispersions are less than 45.51 ps?nm^-1?km^-1. We also show that the proposed fiber has low bend losses thanks to the air-core guidance. The proposed fiber may have applications for data centers and financial network systems that need short-range, large-capacity and low-latency transmission.