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 -olefin of 3 to 20 carbon atoms, having a molar ratio (ethylene/-olefin) of ethylene units to -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 -olefin of 3 to 20 carbon atoms, having a molar ratio (ethylene/-olefin) of ethylene units to -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.