This invention aims to provide lubricating oil compositions excellent in low-temperature properties, oxidation stability, lubricity at high temperatures and fuel efficiency and also in handling properties at low temperatures, and a viscosity modifier for lubricating oil employable in said lubricating oil compositions. The viscosity modifier for lubricating oil comprises an ethylene/&agr;-olefin copolymer (B) composed of: (i) ethylene, (ii) an &agr;-olefin of 3 or more carbon atoms, and (iii) a higher &agr;-olefin of 4 to 20 carbon atoms wherein the carbon number of (iii) is larger than that of (ii) by one or more, and the ethylene/&agr;-olefin copolymer (B) has the following properties (b-1) and (b-2): (b-1) a content of ethylene (i) is in the range of 40 to 80% by weight, a content of the &agr;-olefin of 3 or more carbon atoms (ii) is in the range of 15 to 59% by weight, and a content of the higher &agr;-olefin of 4 to 20 carbon atoms (iii) is in the range of 0.1 to 25% by weight with the proviso that the sum is 100% by weight; and (b-2) a weight-average molecular weight (Mw) in terms of polystyrene as measured by GPC is between 80,000 and 400,000.