To obtain the subject catalyst comprising a solid acid catalyst having a specific pore diameter, free from corrosion resistance to reacting apparatus, excellent in polymerization activity against olefin and selectivity to ≥30C olefin oligomer and useful as automobile engine oil, etc.

This catalyst comprises a solid acid catalyst having 7-15nm average pore diameter, preferably a solid acid catalyst selected from a silica catalyst on which heteropolyacid is supported, a halogenated alumina catalyst, a catalyst as oxide of the group IV metal of the periodic table on which sulfuric acid is supported, a (halogenated) (non) crystalline silica alumina and a (halogenated) alumina boria, especially preferably a solid acid catalyst selected from a silica catalyst on which tungstophosphoric acid is supported, a fluorinated alumina catalyst and zirconium catalyst on which sulfuric acid is supported. The catalyst is preferably obtained by treating alumina, etc., with ammonia fluoride and then, filtering, drying and baking the treated alumina.