The present invention provides a multi-piece solid golf ball having a core obtained by molding under heat a specific rubber composition and having a cover of at least three layers which is composed of a thermoplastic resin material and encases the core. By optimizing the deflection of the core under a specific load, optimizing the hardness at the center of the core and the hardnesses of the innermost cover layer, outermost cover layer and intermediate cover layer, setting the combined thickness of the cover layers to at least a specific value, and forming the innermost cover layer of a highly neutralized ionomer resin composition, the spin rate of the ball on shots taken with a driver can be significantly reduced, enabling the distance traveled by the ball to be increased. Moreover, the ball has a good feel on shots with a driver.