Disclosed is a fluorine-containing copolymer having sufficient stability in water, which is capable of providing paper with sufficient oil resistance. The fluorine-containing polymer contains, as essential components, (a) a fluorine-containing monomer represented by general formula (I) CH2=C(-X)-C(=O)-Y-[-(CH2)m-Z-]p-(CH2)n-Rf (wherein X represents a hydrogen atom Y represents -O- or -NH- Z represents a direct bond, -S- or -SO2- Rf represents a fluoroalkyl group having 1-6 carbon atoms m is a number of 1-10 n is a number of 0-10 and p is 0 or 1) and (b) an alkoxy group-containing monomer represented by general formula (II) CH2=C(X)-C(=O)-O-(RO)q-H (wherein X represents a hydrogen atom or a methyl group R represents an alkylene group having 2-4 carbon atoms wherein a part or all of hydrogen atoms may be substituted by a hydroxyl group and q represent an integer of 1-50). The fluorine-containing polymer does not contain a monomer having an amino group.
