A TBGA (Tape Ball Grid Array) package assembly with grounded heat sink and method of fabricating the same is provided, which is constructed of a tape, a heat sink, and at least one semiconductor chip. The proposed TBGA technology is characterized by that a grounding plug is formed by first forming a via hole in the heat sink and a via hole in the tape without penetrating through the grounding solder-ball pad, and then filling an electrically-conductive material, such as solder or silver paste, into the heat-sink via hole from the top of the package assembly until filling up the tape via hole and the heat-sink via hole. As the semiconductor chip is mounted in position, its grounding pads are electrically bonded to the heat sink, thereby allowing the semiconductor chip to be externally grounded through the grounding plug, the grounding solder-ball pad, and the solder ball attached to the grounding solder-ball pad. The proposed TBGA technology allows the resulted grounding plug to be firmly secured in position due to the filled solder being wettable to the heat sink, thereby providing a greater ball shear strength to the grounding solder ball that is subsequently bonded to the grounding plug. The finished TBGA package would be therefore assured in the reliability of its grounding structure.