Co doped ZnO powders and tablets are synthesized by the solid-state reaction. The X-ray diffraction experimental results indicate that Zn2+ ions are substituted by Co2+ ions. All samples are paramagnetic at room temperature. Using density functional theory (DFT+U) method, the calculated results indicate that the antiferromagnetic ground state of Co2Zn14O16 system is more stable. By calculating the electronic transfers of Co and O atoms, it is indicated that the mechanism of the magnetism tends to the indirect exchange model of Co2+O2-Co2+ bonding in CoZnO system. The direct exchange formula Jpd of Anderson model is modified. Two possible ways to achieve the intrinsic ferromagnetic oxide semiconductor are putted forward.