A novel photonic crystal fiber (PCF) design with two rings of hybrid elliptical air-holes for single-polarization single-mode (SPSM) operation is presented. The proposed SPSM-PCF characteristics are investigated by using a full-vector finite element method (FEM) with perfect matched layer (PML) boundary conditions. The proposed SPSM-PCF can perform a single-polarization single-mode propagation. The modal birefringence of the proposed SPSM-PCF is as high as 0.00284 at the wavelength of 1.55 µm, the beat length is 0.546 mm. The confinement loss of the x-polarized mode is lower than 0.5 dB/km, whereas the loss of the y-polarized one is larger than 15 dB/km. Compared with the case of x-polarized mode, the y-polarized mode can be suppressed with a shorter fiber length. Variations of the mode field characteristics with input wavelength are given. For considering loss ratio and loss difference, the proposed PCF can perform SPSM operation with wide bandwidth of 600 nm. It indicates that this is a good solution to realize single-mode single-polarization operation.