Nowadays, the experimental results of absorption spectrum distribution of Ni doped ZnO suffer controversy when the mole fraction of impurity is in a range from 2.78% to 6.25%. However, there is still lack of a reasonable theoretical explanation. To solve this problem, the geometry optimizations and energies of different Ni-doped ZnO systems are calculated at a state of electron spin polarization by adopting plane-wave ultra-soft pseudo potential technique based on the density function theory. Calculation results show that the volume parameter and lattice parameter of the doping system are smaller than those of the pure ZnO, and they decrease with the increase of the concentration of Ni. The formation energy in the O-rich condition is lower than that in the Zn-rich condition for the same doping system, and the system is more stable in the O-rich condition. With the same doping concentration of Ni, the formation energies of the systems with interstitial Ni and Ni replacing Zn cannot be very different. The formation energy of the system with Ni replacing Zn increases with the increase of the concentration of Ni, the doping becomes difficult, the stability of the doping system decreases, the band gap becomes narrow and the absorption spectrum is obviously red shifted. The Mulliken atomic population method is used to calculate the orbital average charges of doping systems. The results show that the sum of the charge transitions between the s state orbital and d state orbital of Ni2+ ions in the doping systems Zn0.9722Ni0.0278O, Zn0.9583Ni0.0417O and Zn0.9375Ni0.0625O supercells are all closed to +2. Thus, it is considered that the valence of Ni doped in ZnO is +2, and the Ni is present as a Ni2+ ion in the doping system. The ionized impurity concentrations of all the doping systems exceed the critical doping concentration for the Mott phase change of semiconductor ZnO, which extremely matches the condition of degeneration, and the doping systems are degenerate semiconductors. Ni-doped ZnO has a conductive hole polarization rate of up to nearly 100%. Then the band gaps are corrected via the LDA (local density approximation)+U method. The calculation results show that the doping system possesses high Curie temperature and can achieve room temperature ferromagnetism. The magnetic moment is derived from the hybrid coupling effect of p-d exchange action. Meanwhile, the magnetic moment of the doping system becomes weak with the increase of the concentration of Ni. In addition, the absorption spectrum of Ni-interstitial ZnO is blue-shifted in the ultraviolet and visible light bands.