We propose a hole-assisted solid core Bragg fiber (SCBF) with a high-index-contrast cladding for near-infrared broadband single-polarization transmission in this article. The circular symmetry of a common SCBF is broken by the introduced air holes in the solid core for increasing the modal birefringence and polarization-dependent loss (PDL). In the proposed single-polarization SCBF, the confinement of guided modes predominantly depends on the photonic bandgap effect from the high-index-contrast cladding, and simultaneously rests with the total internal reflection from the interface between the solid core and air holes. The numerical results show that both the enhanced modal birefringence and PDL are strongly related to the refractive index, size and locations of air holes. We demonstrate that the modal birefringence for the fundamental mode can be up to the order of 10−3, and the difference in confinement losses between both polarized fundamental modes is no less than an order of magnitude, which is sufficiently large to support single-polarization operation. Moreover, the single-polarization bandwidth with the transmission loss lower than 0.1 dB/m is as high as 277 nm and the critical bend radius is as low as 1 cm, indicating the excellent performances of high bandwidth and bending resistance in the hole-assisted single-polarization SCBF.