Based on first-principles calculations, we study the magnetic properties of Co, Ni, Fe, V, and Mn impurities in ZnO. The stabilities of the ferromagnetic state and the magnetic moment of each impurity largely depend on the amount of doped electron or hole. For lightly doped n-type ZnO, it is found that the doping of Ni ions is the most effective for inducing ferromagnetism, while Fe ions show the most stable ferromagnetic couplings for heavily doped n-type samples. The characteristics of the magnetic interactions of Co ions are similar with those of Fe ions, but Co ions require much larger amount of doped electron than Fe ions to show the ferromagnetic couplings. The ferromagnetic coupling between Mn and V ions is unstable in n-type conditions.