A single-polarization single mode optical fiber of the type comprising an elliptical core, a pair of stress applying parts on both sides of the minor radius of the elliptical core for applying asymmetrical stress thereto and a clad embedding therein the core and the stress applying parts, the stress applying parts being made of B.sub.2 O.sub.3 wherein a relative refractive index difference .DELTA. between the core and the clad satisfies a relation 0.004.ltoreq..DELTA..ltoreq.0.05, an ellipticity .epsilon. satisfies a relation 0.01.ltoreq..epsilon..ltoreq.0.9, the B.sub.2 O.sub.3 has a molar concentration of 1 to 25 mole %, ratio of thickness of the stress applying parts and the core is 5 to 15, a modal birefringence B expressed by an equation B=(.beta..sub.x -.beta..sub.y)/k satisfies a relation B=1.times.10.sup.-6 where (.beta..sub.x -.beta..sub.y) represents a propagation constant difference between HE.sub.11.sup.x and HE.sub.11.sup.y modes, and k a wave number in vacuum, whereby a polarization mode dispersion, that is a delay time difference between the HE.sub.11.sup.x and HE.sub.11.sup.y modes which are orthogonal with each other is zero.