The present invention provides an olefin block copolymer for a viscosity index improver capable of preparing a lubricating oil composition having excellent low temperature properties and excellent balance between viscosity and shear stability, a viscosity index improver and a lubricating oil composition comprising the viscosity index improver.The olefin block copolymer has a Mw / Mn of not more than 1.5, and comprises:(i) a polymer block comprising ethylene and an α-olefin of 3 to 20 carbon atoms, having a molar ratio (ethylene / α-olefin) of ethylene units to α-olefin units of from 20 / 80 to 65 / 35, a Mw of 50,000 to 2,000,000, and having a slope of an intramolecular composition distribution of absolute value of 0.1 to 0, and(ii) a polymer block comprising ethylene and an α-olefin of 3 to 20 carbon atoms, having a molar ratio (ethylene / α-olefin) of ethylene units to α-olefin units of from 70 / 30 to 85 / 15, a Mw of 10,000 to 400,000, and having a slope of an intramolecular composition distribution of absolute value of 0.1 to 0.