In a multi-piece solid golf ball comprising a solid core consisting of a center core and an outer core, an inner cover layer and an outer cover layer, the solid core is molded from a rubber composition comprising a base rubber composed of (a) a polybutadiene having a high cis-1,4 content, a minimal 1,2 vinyl content and a viscosity η of up to 600 mPa·s at 25° C. as a 5 wt % toluene solution, being synthesized using a rare-earth catalyst, in combination with (b) another diene rubber, (c) an unsaturated carboxylic acid, (d) an organosulfur compound, (e) an inorganic filler, and (f) an organic peroxide; and the center core has a specific JIS-C hardness on its center and a specific JIS-C hardness on its surface and the certain difference, the outer core is harder than the surface hardness of the center core, the cross-sectional hardness of 1 mm outside from the border between the center core and the outer core is a specific range on JIS-C hardness, the surface of the outer core has a specific JIS-C hardness, the inner cover layer has a specific Shore D hardness; the outer cover layer has a specific Shore D hardness; and the outer cover layer has a lower Shore D hardness than the inner cover layer. This combination of features gives the ball a good, soft feel upon impact and an excellent spin performance that provides increased distance.