The lubricating oil composition of the invention comprises a lubricating oil base (A) and a copolymer (B) of ethylene and an alpha-olefin of 3 to 20 carbon atoms. The copolymer (B) of ethylene and an alpha-olefin of 3 to 20 carbon atoms is contained in the composition in an amount of 1 to 20% by weight and has the following properties:(1) the ethylene content (E) is in the range of 40 to 77% by weight,(2) the weight-average molecular weight (Mw) in terms of polystyrene, as measured by GPC, is in the range of 80,000 to 400,000,(3) Mw / Mn is not more than 2.4,(4) the melting point (Tm), as measured by DSC, is not higher than 60° C.,(5) the ethylene content (E, % by weight) and the melting point (Tm, ° C.), as measured by DSC, satisfy the following relation (I):and(6) the intensity ratio, Salphabeta / Salphaalpha, measured by 13C-NMR spectrum is not more than 0.5.