Co doped ZnO powders were synthesized by the solid-state reaction. The magnetic and optical properties of the powders were investigated. The experimental results indicate that Zn2+ ions were substituted by Co2+ ions randomly. Zn0.95Co0.05O powders prefer paramagnetic state to ferromagnetic state from 3 K to 300 K due to coupling exchange interactions between Co 3d spins, which makes the nearest Co2+ antiparallel.