We propose a meniscoid nested anti-resonant hollow-core fiber (MAF), wherein the fourfold rotational symmetry structure enables high birefringence and low loss in dual-wavelength range. Numerical investigation and simulation for variations in wall thickness along orthogonal directions are conducted, through which a formulated optimization criterion revealing the relationship between minimum difference in wall thickness and birefringence of 10−5 is obtained. A parameter of beat length to loss ratio η is defined to evaluate MAF performance with respect to birefringence and confinement loss (CL). With optimized MAF structure, the birefringence and CL are improved to 3.62 × 10−5 and 8.5 dB/km at 1.06 µm, 9.83 × 10−5 and 204.1 dB/km at 1.55 µm, respectively. Meanwhile, the bandwidths extend to 172 nm at 1.06 µm and 216 nm at 1.55 µm, and the superior bending resistance characteristics are validated. Our work offers valuable guidance for designing and optimizing highly birefringent anti-resonant hollow-core fiber (ARF), and the proposed MAF has great potential in polarization-dependent transmission and interferometric fiber gyroscopes.