The present invention provides a process for producing a saturated aliphatic hydrocarbon prepared using an α-olefin as a raw material and represented by the general formula (1), including the steps of: (I) producing a vinylidene olefin by dimerizing the α-olefin in the presence of a metallocene complex catalyst; (II) further dimerizing the vinylidene olefin in the presence of an acid catalyst; and (III) hydrogenating the obtained dimer. Further, there are provided a lubricant composition containing the saturated aliphatic hydrocarbon compound produced by the above process, a bearing oil consisting of the lubricant composition, and making use of the same, a bearing and gyral equipment. The saturated aliphatic hydrocarbon compounds produced by the process of the present invention have low-temperature fluidity, exhibiting low evaporativity, and excellent in thermal stability and oxidation stability. Thus, the saturated aliphatic hydrocarbon compounds are suitable for use as, for example, a base oil of lubricant composition for hydraulic pressure, turbine, working machine, bearing, gear, metal-working, etc.