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This paper presents a structure to realize a planar dual-band omni-directional antenna. Firstly, the omnidirectional resonant modes of a circular and a ring patch antenna are found by theoretical calculation. Next, by a simulation program, IE3D, the calculated modes are checked, and moreover, the resonant frequencies are tuned to the desired ones. Then, the antenna is realized by the printed-circuit board process. The circular and ring antenna are laid out together concentrically and combined to be fed by a power divider. The measured radiation patterns of lower band (2.43GHz) and higher band (5.5GHz) are quite to meet the omni-directional requirement.