PURPOSE: To provide a lubricating base oil having a high viscosity index and a low pour point by contacting as feedstock, which contains the hydrocrackate of a wax-containing mineral oil fraction, with a catalyst under dewaxing conditions.

CONSTITUTION: The target lubricating base oil is provided by contacting the feedstock containing at least part of the hydrocrackate of the wax-containing mineral oil fraction, which contains paraffin hydrocarbons more than 50 wt.%, and having the dynamic viscosity of less than 10 mm2/g at 100°C with the dewaxing catalyst preferably under the dewaxing conditions of a temperature of from 200° to 450°C and a spatial velocity of from 0.1 to 5.0 kg/l catalyst.h. In this case, as the dewaxing catalyst, a zeorite catalyst containing a composite crystal aluminium silicate is especially preferable.