A compact single-polarization (SP) coupler based on a dual-hollow-core anti-resonant fiber (DHC-ARF) is proposed. By introducing a pair of thick-wall tubes into a ten-tube single-ring hollow-core anti-resonant fiber, the core is separated into two cores to form the DHC-ARF. More importantly, by introducing the thick-wall tubes, dielectric modes in the thick wall are excited to inhibit the mode-coupling of secondary eigen-state of polarization (ESOP) between two cores while the mode-coupling of the primary ESOP can be enhanced, and thus the coupling length (Lc) of the secondary ESOP is greatly increased and that of primary ESOP is reduced to several millimeters. Simulation results show that the Lc of the secondary ESOP is up to 5549.26 mm and one of the primary ESOP is only 3.12 mm at 1550 nm through optimizing fiber structure parameters. By using a 1.53-mm-long DHC-ARF, a compact SP coupler can be implemented with a polarization extinction ratio (PER) less than - 20 dB within the wavelength range from 1547 nm to 1551.4 nm, and the lowest PER of - 64.12 dB is achieved at 1550 nm. Its coupling ratio (CR) is stable within 50 ± 2% in the wavelength range from 1547.6 nm to 1551.4 nm. The novel compact SP coupler provides a reference for developing HCF-based polarization-dependent components for use in the high-precision miniaturized resonant fiber optic gyroscope.