A novel dual-hollow-core anti-resonant fiber (DHC-ARF) with silicon layers and nested resonant tubes is proposed for constructing a 3 dB single-polarization coupler. High-index silicon layers are deposited inside four cladding tubes along the x-direction and then nested resonant tubes are introduced into these cladding tubes, which is beneficial to promote the mode coupling between the x-polarized fundamental mode and the dielectric mode in the silica/silicon tubes so as to achieve single-polarization characteristics of the DHC-ARF. The properties of the DHC-ARF are optimized using finite element method combined with perfectly matched layer as a boundary condition. By using a 1.51 cm long DHC-ARF, a single-polarization 3 dB coupler is constructed with a relatively wide bandwidth of 29 nm covering the wavelength range from 1530 nm to 1559 nm, in which the polarization extinction ratio (PER) is lower than -20 dB and the coupling ratio can be guaranteed within 50 ± 2%. This bandwidth is more than 2.6 times higher than the bandwidth of currently reported single-polarization coupler. At the wavelength of 1550 nm, the lowest PER reaches -74.8 dB and the loss of the coupler is as low as 0.33 dB.