Zn0.98Cu0.020 powders are prepared by the sol-gel method. A small number of CuO impurity phases are observed by the x-ray diffraction, indicating the solubility of Cu in ZnO is less than 2 at.%. The Zn0.98Cu0.020 powders exhibit diamagnetism at 300 K and paramagnetism at 5 K. After subtracting the diamagnetic contribution of ZnO bulk and the paramagnetic contribution of defects, Cu ions exhibit weak paramagnetism. By codoping Cu with Co or Mn in ZnO, only paramagnetism is observed at room temperature.