A ball grid array semiconductor package is proposed, wherein at least a chip is mounted on a substrate, and signal pads on the chip are electrically connected to signal fingers on the substrate by bonding wires. A power plate and a ground plate are each attached at two ends thereof respectively to predetermined positions on the chip and substrate, without interfering with the bonding wires. No power ring or ground ring is necessarily formed on the substrate, thereby reducing restriction on trace routability of the substrate. Further, with no provision of power wires or ground wires, short circuit of the bonding wires is less likely to occur, and thus production yield is enhanced. In addition, the power plate and ground plate provide shielding effect for protecting the chip against external electric-magnetic interference, and are partly in direct contact with the atmosphere for improving heat dissipating efficiency of the semiconductor package.