The polarization mode dispersion (PMD) in a single mode fiber caused by eccentricity of refractive index distribution of core and clad is analyzes and calculates considering that arbitrary uncircularity is equivalent to the ellipse. The relative curves of the difference of propagation constants Δ β and PMD versus the ratio of eccentricity, wavelength, radius of core and difference of refractive index are obtained. It can offer a theoretic guidance for decreasing the PMD in a single mode fiber. The PMD caused by eccentricity has the same magnitude with that caused by ellipticity.