The present invention is directed to a golf ball comprising a dual core, a triple core, a cellular core, a liquid core, or a wound core; an inner cover layer and an outer cover layer; and at least 50 parts by weight of a non-ionomeric polyolefin material disposed in an inner layer within the ball. The dual or triple cores comprise an interior spherical center component formed from a thermoset material, a thermoplastic material, or combinations thereof; a core layer disposed about the center component, formed from a thermoset material, a thermoplastic material, or combinations thereof; and an optional outer core layer that surrounds the core component. The inner cover layer is comprised of a high acid ionomer or ionomer blend. The outer cover layer is comprised of a soft, very low modulus ionomer or ionomer blend, or a non-ionomeric thermoplastic elastomer such as polyurethane, polyester or polyesteramide. The resulting multi-layered golf ball of the present invention provides for enhanced distance without sacrificing playability or durability when compared to known multi-layer golf balls.