We propose a weakly coupled polarization-maintaining few-mode fiber (PM-FMF) design with elliptical-core and bow-tie stress-applying areas. Using a high refractive index core, the proposed fiber can support 32 independent eigenmodes in the 1505-1585 nm band. The combination of the elliptical-core and bow-tie stress-applying area effectively separates the adjacent eigenmodes. The structural parameters of the elliptical-core and the bow-tie stress-applying area of the PM-FMF are optimized using the finite element method. The effects of fiber parameters on the number of modes, the minimum effective refractive index difference (Δn_{eff, mim}) between modes, the mode birefringence B_m, the stress birefringence B_s, and the bending loss are evaluated. The bandwidth performance of the fiber is also analyzed, including the effective refractive index n_eff, Δn_eff and differential mode delay (DMD) between adjacent modes. The results indicate that 32 eigenmodes supported by the fiber are completely separated with Δn_{eff, min} between adjacent modes larger than 1.295×10^-4 in the 1505-1585 nm band. The fiber proposed can improve the transmission capacity and has potential applications in eigenmode multiplexing transmission.