Provided is an optical glass fiber coating composition which when coated on an optical glass fiber and suitably cured provides a coating having the combination of properties (i) through (iv):(i) a stable tensile modulus that is low at room temperature and over a broad range of temperatures below room temperature,(ii) an adhesion to the optical glass fiber sufficient to prevent structural defects and microbending in the optical glass fiber,(iii) the capability of being removed by stripping from the optical glass fiber substantially no residue left on the optical glass fiber, and(iv) which satisfies each of the following inequalities (I) and (II),X.ltoreq.0.2 kg/mm.sup.2 (I)X/Y.gtoreq.1/10 (II) wherein X is the tensile modulus (kg/mm.sup.2) measured at 23.degree. C. and Y is the tensile modulus (kg/mm.sup.2) measured at -40.degree. C.,This coating composition comprises:(A) a urethane (meth)acrylate formed from,(a) a diol compound containing at least one structure represented by one of the following formulas (1) and (2), ##STR1## (b) a compound containing two isocyanate groups, and (c) a compound containing a (meth)acrylate group and a hydroxy group;(B) a second (meth)acrylate-containing compound of which the homopolymer has a glass transition temperature of at most about 0.degree. C.; and(C) a polymerization initiator.