Passive RFID tag, which has not battery, receives the power for it’s activation from the reader antenna only. In this system, when a tag is attached at the surface of the liquid product having high permittivity, read range is short significantly for decreasing the supplied power to the tag antenna caused by the attached material. A theoretical analysis of degrading parameters for a tag antenna due to the attached material is presented and compared with measured values. From this result, an estimation method of maximum read range is presented at the position located on a tag. And the passive RFID tag antenna, which has the helical structure and read range of maximum 1.7m, is suggested. It is suited to attach the plastic lid. And it has the specifications which are -5dB frequency bandwidth of 2.3MHz(resonate frequency at 912MHz) and the fabricated size of radius of 1.5cm, height of 0.8cm and directional radiation pattern. The supposed structure can be applied in Europe, Japan, and Korea adopting the narrow bandwidth.