Negative refractive index (NRI) of the quantized lossless mesoscopic left-handed transmission line (LHTL) is deduced numerically in thermal Fock state. Some specific quantum features of NRI dependent the temperature, frequency of the electromagnetic wave and photon numbers, and quantum fluctuations are shown in the lossless LHTL. The results are significant for the miniaturizing applications of LHTL and quantum circuits. Keywords Negative refractive index · Mesoscopic Left-handed transmission lines · Thermal Fock state 1 Introduction The theoretical speculation of negative refractive index materials (NRM) proposed by V. Veselago[1] in 1968, in which several fundamental phenomena occurring in or in association with NRM were predicted, such as the negative Goos-Hänchen shift[2], amplification of evanescent waves[3], reversals of both Doppler shift and Cerenkov radiation[1], sub-wavelength focusing[4] and so on. Some typical approaches for NRM can be summarized as artificial structures such as metamaterials[5-7] and photonic crystals[8-10], chiral materials[11] and photonic resonant media[12, 13]. Although very exciting from a physics point of view, the artificial structures seem to be of little practical interest for engineering applications because