A fluorine-containing elastomer for molding fuel system parts, which has a copolymer composition comprising 10-40% by weight of tetrafluoroethylene (TFE), 80-30% by mole of vinylidene fluoride (VdF), and 10-30% by mole of hexafluoropropylene (HFP), as copolymerized in the presence of an iodine and bromine-containing compound represented by the following general formula: RBrnIm (where R is a fluorohydrocarbon group, a chlorofluorohydrocarbon group, or a hydrocarbon group, each having 1-10 carbon atoms, and n and m each are 1 or 2), and has an intrinsic viscosity of 20-180 ml/g, Mw (weight average molecular weight)/Mn (number average molecular weight) ratio of 2-20, and a molecular weight distribution of monopeak or multipeak type, and a fluorine-containing elastomer composition, which comprises the fluorine-containing elastomer, at least one of a polyol vulcanizing agent and a polyamine vulcanizing agent, an organic peroxide, and a polyfunctional unsaturated compound. The composition is suitable for use in molding fuel system parts to give fluorine-containing elastomer moldings with distinguished moldability, vulcanizate physical properties, chemical resistance, photostability and economy.