A method of fabricating a BGA (Ball Grid Array) IC package of the type having an encapsulating body is proposed, which allows the BGA IC package to be manufactured without having to use conventional organic substrate and encapsulating-body mold having cavity, so that the manufacture process can be more cost-effective to carry out than the prior art. The proposed method is characterized in the use of a copper piece which is selectively removed to form an encapsulating-body cavity for the forming of an encapsulating body therein. The proposed method requires no use of mold with cavity for the forming of the encapsulating body, allowing the same mold to be used for the fabrication of various BGA IC packages of different sizes. Moreover, the proposed method allows fan-in design as well as fan-out design, thus allowing the number of I/O ports to be increased while making the overall package configuration compact in size, and also allows the implantation of the electrically-conductive balls to be easier to carry out and more precisely controlled than the prior art, making the ball implantation more assured in quality than the prior art. Therefore, the proposed method is more advantageous and cost-effective to use than the prior art.