Hollow-core negative curvature fibers (HC-NCFs) have become one of the research hotspots in the field of optical fiber because of their potential applications in the data and energy transmissions. In this work, a new kind of single-polarization single-mode HC-NCF with nested U-type cladding elements is proposed. To achieve the single-polarization single-mode transmission, we use two different silica tubes in thickness, which satisfy the resonance and anti-resonance conditions on the U-type cladding elements and the cladding tubes, respectively. Besides, the elliptical elements are introduced to achieve good single-mode performance. By studying the influences of the structure parameters on the propagation characteristics, the optimized structure parameters are obtained. The simulation results show that when the wavelength is fixed at 1550 nm, the single-polarization single-mode transmission is achieved, with the polarization extinction ratio of 25749 and minimum high-order mode extinction ratio of 174. Furthermore, the confinement loss is only 0.0015 dB/m.