A quench protection system for a high-temperature superconducting (HTS) coil using Cu tape co-wound with an HTS tape was studied by numerical analysis using a thermal model of a coil winding pack. In normal operation, the voltage across the resistive zone Vs in the HTS coil was monitored by measuring the voltage difference between the HTS coil and the co-wound Cu coil. When Vs exceeded the quench detection voltage, the HTS coil was disconnected from the power supply and the energy stored in the HTS coil was dumped into a dump resistor. At the same time, the terminals of the co-wound coil were connected to another resistor, and some of the current in the HTS coil was quickly transferred to the co-wound Cu tape coil due to the tight magnetic coupling of both coils. This is expected to decrease the hot-spot temperature due to the quick decrease of HTS coil current and to protect the coil from damage caused by overheating at the hot-spot. The analysis investigated the effectiveness of this method.