The invention provides a multi-piece solid golf ball having a solid core, at least one intermediate layer and a cover. The core has a hardness which gradually increases from a core center to a core surface, with the golf ball having specific values for the hardness difference between the core center and the core surface; the hardness difference (I)-(II) in JIS-C hardness units being not more than ±2; the (hardness of intermediate layer material)−(hardness of core surface); the (initial velocity of sphere composed of core encased by intermediate layer)−(initial velocity of core); the (deflection of sphere composed of core encased by intermediate layer)/(deflection of core); and the (hardness of cover material)−(hardness of intermediate layer material).