A peroxide-crosslinkable fluorine-containing elastomer IS produced by subjecting a fluorine-containing olefin and a perfluoroalkyl divinyl ether monomer represented by the general formula: CF2═CF—[OCF2CF(CF3)]aO(CF2)bO[CF(CF3)CF2O]c—CF═CF2 wherein a+c is an integer of 0 to 4 and b is an integer of 2 or more, to a copolymerization reaction; wherein the perfluoroalkyl divinyl ether monomer is added for copolymerization separately before and after the copolymerization reaction starts, or the total amount thereof is added for copolymerization after the copolymerization reaction starts. A peroxide-crosslinked molded product of the obtained fluorine-containing elastomer exhibits high compression set characteristic, while reducing a decrease in breaking strength, a decrease in elongation at break or an increase in hardness.