A multi-piece solid golf ball has a solid core obtained by molding and vulcanizing a rubber composition which includes (A) a base rubber containing a polybutadiene synthesized using a rare-earth catalyst, (B) an unsaturated carboxylic acid and/or a metal salt thereof, (C) an organic sulfur compound, (D) an inorganic filler and (E) an organic peroxide. The core is enclosed within a mantle of one or more layer which is made primarily of a thermoplastic resin and has a Durometer D hardness of 30 to 70. The mantle is enclosed within a cover which is made primarily of a thermoplastic polyurethane and which has a Durometer D hardness of 40 to 60 that is lower than the Durometer D hardness of the outermost layer of the mantle. This construction provides the golf ball with an outstanding rebound.