A novel hollow-core anti-resonant fiber based on a dual-tube structure with nested tubes was proposed and numerically studied for near-infrared single-polarization single-mode operation. Unlike conventional anti-resonant structures with polygonal cladding tubes, the proposed fiber consists of two identical thin-walled tubes symmetrically positioned within the outer cladding, each internally nested with a slightly smaller radius tube. The introduction of the nested tubes enhances the confinement loss of higher-order modes, thereby enabling the fiber to achieve single-polarization single-mode operation. Simulation results demonstrate that the fiber exhibits single-polarization characteristics across the wavelength range of 1450 nm to 1700 nm, and single-polarization single-mode operation within the range of 1639 nm to 1672 nm, with a bandwidth of 33 nm. This fiber design holds significant potential for the development of high-performance single-polarization single-mode fiber devices.