A semiconductor package with a heat dissipating structure is provided, including a lead frame with a die pad for allowing a chip to be mounted on an upper surface of the die pad, and a heat sink abutting against a lower surface of the die pad. A top surface of the heat sink, in contact with the lower surface of the die pad, is formed with at least a recessed portion. During a molding process of using a resin material to form an encapsulant for encapsulating the chip, lead frame and heat sink, the resin material fills into the recessed portion and forms a supporting member between the die pad and heat sink to provide support for a central portion of the die pad, so as to prevent the chip from cracking in a step of building up a packing pressure of the molding process, thereby assuring yield and reliability of fabricated products.