PURPOSE: To obtain a lube base oil having a high viscosity index and improved in light stability and heat stability by hydrocracking heavy gas oil and/or vacuum gas oil to give a residual oil and subjecting the residual oil to dewaxing and solvent extraction after removing a high boiling fraction therefrom.

CONSTITUTION: Heavy gas oil and/or vacuum gas oil is hydrocracked under the conditions of a pressure of 70-150kg/cm2, a temperature of 350-450°C, a liquid space velocity of 0.2-3hr-1, and a hydrogen feed rate of 500-2,000m3/kl to give a residual oil having a boiling point of 280°C or higher. The residual oil is distilled to remove a fraction having a boiling point of 484-488°C, dewaxed with a solvent mixture comprising, e.g. methyl ethyl ketone and toluene, and then subjected to vacuum distillation to remove a low boiling fraction and a high boiling fraction, thus giving a lube base oil which does not contain a fraction having a boiling point of 484-488°C and has a viscosity index of 105 or higher and a kinematic viscosity of 7-45cSt at 40°C.