In a multi-piece solid golf ball comprising a solid core, an enclosure layer, an intermediate layer, and a cover, the enclosure layer and the intermediate layer each have a Shore D hardness of 10-50, the hardness of the intermediate layer is lower than that of the enclosure layer, and the deflections under a load of 100 kg of the solid core, a first spherical body consisting of the solid core and the enclosure layer, a second spherical body consisting of the solid core, the enclosure layer and the intermediate layer, and the ball are controlled to fall in specific ranges. The cover is formed of a cover stock comprising an ionomer resin and an inorganic filler.