At present, the effects on the magnetic and electrical properties of Cu heavily doped ZnO with the mole amount of Cu being in a range of 0.02778-0.16667 are rarely studied by first-principles. Therefore two models for Zn1-xCuxO supercells (x=0.02778, 0.03125) are set up to calculate the band structures and density of states by using the plane-wave ultrasoft pseudopotential based on the spin-polarized density functional theory. The calculation results indicate that the doped systems are degenerate semiconductors, and they are semimetal diluted magnetic semiconductors. As the doping amount of Cu increases, the relative concentration of free holes increases, the effective mass of holes decreases, the electron mobility decreases and the electronic conductivity increases. These results are validated again by the analysis of ionization energy and Bohr radius, and they are consistent with the experimental data. As the doping amount of single-Cu increases from 0.02778 to 0.0625, the volume of doping system decreases, the total energy increases, the stability decreases, the formation energy increases and doping is more difficult. As the same concentration and the different doping modes for double-Cu doped, the magnetic moment of doping system first increases and then decreases with the increasing of spacing of Cu-Cu; while the bonds of nearest Cu–O–Cu lie along the a-axis or b-axis, the magnetic moment of doping system disappears; while the bonds of nearest Cu–O–Cu lie along the c-axis, the Curie temperature reaches a temperature above room temperature. As the doping amount of double-Cu increases from 0.0625 to 0.16667, the total magnetic moment of doping system first increases and then decreases, while the bonds of nearest Cu–O–Cu lie along the c-axis. The calculation results are consistent with the experimental data.