The invention provides a multi-piece solid golf ball having a solid core encased by a cover of one, two or more layers, the solid core including a spherical first layer, a second layer encasing the first layer and a third layer encasing the second layer. The first layer has a diameter of from 3 to 24 mm, and the third layer is formed of a rubber composition composed primarily of polybutadiene rubber. The ball has specific relationships between the cross-sectional hardness at the core center on a cut face when the solid core has been cut in half and the respective hardnesses of the first layer 1 mm inside an interface between the first layer and the second layer, the second layer 1 mm outside the interface between the first layer and the second layer, the second layer 1 mm inside an interface between the second layer and the third layer, the third layer 1 mm outside the interface between the second layer and the third layer, and the surface of the third layer. Such a golf ball has both a reduced spin rate and a good initial velocity on shots, particularly when struck in a high head-speed range, and thus is able to achieve an increased distance, in addition to which it is also capable of having a good feel on impact.