In a multi-piece solid golf ball having a core, a cover and an intermediate layer therebetween, the core, an intermediate layer-encased sphere and the ball have surface hardnesses which satisfy a specific relationship, and the intermediate layer and the cover have thicknesses which satisfy a specific relationship. Also, the core has a hardness profile in which the hardnesses at the core surface, core center, a position 5 mm from the core center, and a position midway between the surface and center of the core satisfy specific relationships. This golf ball, when used by mid- and high-level amateurs, enables the golfer to maintain an adequate distance on shots with a driver and achieve a good distance on iron shots, has a good spin performance on approach shots and has a good feel on impact. In addition, the ball has an excellent scuff resistance when struck with a grooved wedge.