In a multi-piece solid golf ball comprising a solid core and a cover of two inner and outer layers enclosing the solid core, the solid core has a deflection of at least 1.1 mm under an applied load of 294 N (30 kgf) and a surface and a center, the surface-center hardness difference given as a JIS-C hardness at the core surface minus a JIS-C hardness at the core center is up to 15 units, the cover inner layer is formed of a resin composition comprising as essential components, (a) an olefin-unsaturated carboxylic acid random copolymer, an olefin-unsaturated carboxylic acid-unsaturated carboxylate random copolymer, a metal ion neutralized product of each copolymer, or a mixture of each copolymer and the neutralized product, (b) a fatty acid having a molecular weight of at least 280 or derivative thereof, and (c) a basic inorganic metal compound capable of neutralizing acid groups in components (a) and (b), the Shore D hardness of the cover inner layer, the Shore D hardness of the cover outer layer, and the hardness relationship between the cover inner layer and the cover outer layer are adjusted, and the sum of dimple trajectory volumes each obtained by multiplying the volume of a dimple by the square root of a dimple diameter is optimized.