A semiconductor package with a lead frame as a chip carrier and a method for fabricating the same are provided. The lead frame includes a die pad and a plurality of leads properly spaced apart from the die pad, each lead being composed of an inner lead portion and an outer lead portion, wherein the inner lead portion is directed toward the die pad, and the outer lead portion has a terminal. At least a chip is mounted on the die pad, and a first encapsulant is formed for encapsulating the chip, die pad and inner lead portions. An injection-molded second encapsulant is formed for encapsulating the first encapsulant and outer lead portions, but exposing the terminals of the outer lead portions. The second encapsulant made by injection molding can prevent resin flash over the exposed terminals, thereby assuring electrical-connection quality of the semiconductor package.