The invention provides a solid phosphoric acid catalyst which has high activity and attains high dimer selectivity in olefin dimerization reactions and efficient methods of olefin dimerization. The solid phosphoric acid catalyst comprises a carrier and phosphoric acid supported thereon. When the solid phosphoric acid catalyst is heated at 250° C. for 20 minutes, heating loss of water is 50 mass % or more based on diphosphorus pentoxide (P2O5) derived from the phosphoric acid. A method of olefin dimerization comprises bringing an olefin-containing feed material containing water in an amount of 10-1000 mass ppm into contact with the catalyst to initiate the reaction.