The spin effect on a single-mode single-polarization optical fiber is investigated theoretically and numerically. To get a practical single elliptically polarized fiber the normalized spin rate must be in the range of 0.2–0.35. A single elliptically polarized fiber with a normalized spin rate around 0.224 is demonstrated. It has a broad band from 1.530 to 1.558 μm, in which the low-leakage elliptically polarized eigenmode loss is kept within 1.2 dB while the high-leakage elliptically polarized eigenmode loss is greater than 20 dB. This fiber can be used as an elliptical polarizer or applied in current sensing.