Hole carrier mediated magnetization in Cu-doped GaN is investigated by using the first-principles calculations. By studying the sp-d interaction and the direct exchange interaction among the dopants, we obtain an equation to determine the spontaneous magnetization as a function of the Cu dopant concentration and the hole carrier density. It is demonstrated that nonmagnetic Cu doped GaN can be of room-temperature ferromagnetism. The system's Curie temperature Tc can reach about 345 K with Cu concentration of 1.0% and hole carrier density of 5.0×10^19 cm-3. The results are in good agreement with experimental observations and indicate that ferromagnetism in this systems is tunable by controlling the Cu concentration and the hole carrier density.