Composition for lubricating a compression-type refrigerator using a hydrofluorocarbon refrigerant, comprising: a) a lubricating oil comprising 70% by mass or more of a polyvinyl ether-based compound containing in the molecule an alkylene glycol unit or a polyoxyalkylene glycol unit and a polyvinyl ether unit and having a molecular weight in the range of 300-3,000 and a structure represented by the general formula wherein R 1, R 2 and R 3 each represent a hydrogen atom or a C 1 to C 8 hydrocarbon group and may be the same as or different from each other, R b represents a divalent C 2-4 hydrocarbon group, R a represents a hydrogen atom, a C 1-20 aliphatic or alicyclic hydrocarbon group, a C 1-20 aromatic group which may have a substituent, a C 2-20 acyl group or a C 2-50 oxygen-containing hydrocarbon group, R 4 represents a C 1-10 hydrocarbon group, with the proviso that when there are a plurality of R a 's, a plurality of R b 's and a plurality of R 4 's, the R a 's, R b 's and R 4 's may each be the same as or different from each other, m is a number of 2-50 on average, k is a number of 1-10 on average, and p is a number of 2-25 on average, with the provisos that when there are a plurality of k's and a plurality of p's, the distribution may each be block or random, and that when there are a plurality of R b O's, the R b O's may be the same as or different from each other, and b) a hydrofluorocarbon refrigerant, wherein the hydrofluorocarbon refrigerant is a fluorinated hydrocarbon having a double bond alone or a combination of a saturated fluorinated hydrocarbon and a fluorinated hydrocarbon having a double bond a) a lubricating oil comprising 70% by mass or more of a polyvinyl ether-based compound containing in the molecule an alkylene glycol unit or a polyoxyalkylene glycol unit and a polyvinyl ether unit and having a molecular weight in the range of 300-3,000 and a structure represented by the general formula wherein R 1, R 2 and R 3 each represent a hydrogen atom or a C 1 to C 8 hydrocarbon group and may be the same as or different from each other, R b represents a divalent C 2-4 hydrocarbon group, R a represents a hydrogen atom, a C 1-20 aliphatic or alicyclic hydrocarbon group, a C 1-20 aromatic group which may have a substituent, a C 2-20 acyl group or a C 2-50 oxygen-containing hydrocarbon group, R 4 represents a C 1-10 hydrocarbon group, with the proviso that when there are a plurality of R a 's, a plurality of R b 's and a plurality of R 4 's, the R a 's, R b 's and R 4 's may each be the same as or different from each other, m is a number of 2-50 on average, k is a number of 1-10 on average, and p is a number of 2-25 on average, with the provisos that when there are a plurality of k's and a plurality of p's, the distribution may each be block or random, and that when there are a plurality of R b O's, the R b O's may be the same as or different from each other, and R 1, R 2 and R 3 each represent a hydrogen atom or a C 1 to C 8 hydrocarbon group and may be the same as or different from each other, R b represents a divalent C 2-4 hydrocarbon group, R a represents a hydrogen atom, a C 1-20 aliphatic or alicyclic hydrocarbon group, a C 1-20 aromatic group which may have a substituent, a C 2-20 acyl group or a C 2-50 oxygen-containing hydrocarbon group, R 4 represents a C 1-10 hydrocarbon group, with the proviso that when there are a plurality of R a 's, a plurality of R b 's and a plurality of R 4 's, the R a 's, R b 's and R 4 's may each be the same as or different from each other, m is a number of 2-50 on average, k is a number of 1-10 on average, and p is a number of 2-25 on average, with the provisos that when there are a plurality of k's and a plurality of p's, the distribution may each be block or random, and that when there are a plurality of R b O's, the R b O's may be the same as or different from each other, and b) a hydrofluorocarbon refrigerant, wherein the hydrofluorocarbon refrigerant is a fluorinated hydrocarbon having a double bond alone or a combination of a saturated fluorinated hydrocarbon and a fluorinated hydrocarbon having a double bond