A process for producing a polymer of an null-olefin which comprises polymerizing an null-olefin having at least 4 carbon atoms in the presence of a catalyst for producing polymers of olefins which comprises (A) a specific metal compound and (B) at least one compound selected from (b-1) an organoaluminum oxy compound and (b-2) an ionic compound. The polymer of an null-olefin is useful as a component of lubricant.