PURPOSE:To obtain an optical fiber excellent in its strength and flexibility without lowering its light transmission performance by drawing a composite-spun optical fiber precursor up to its specified time length. CONSTITUTION:A polymer, shown by the formula, having alkyl ester fluoride of alpha,beta-unsaturated monocarboxylic acid as its main constituent used as a core, and a copolymer of perfluoro(2,2-dimethyl-1,3-dioxol) and at least one copolymerizable ethylene unsaturated monomer is used as a sheath. The difference in glass transition temperature between both polymers is made less than 30 deg.C. An optical fiber is preferably the obtained fiber is drawn, the temperature is made higher than the glass transition temperature by 10-30 deg.C, and the drawing ratio is set 1.2-10 times, preferably 1.5-5 times. The optical fiber thus becomes tough and highly flexible.