Negative refractive index (NRI) of the mesoscopic dissipative left-handed transmission line (LHTL) is manipulated by the displaced squeezed Fock state and the dissipation presented by the resistance and conductance.Compared with the classical LHTL,some novel characteristics of NRI are shown in the LHTL because of the quantum effect,which will be significant for its miniaturization application in microwave frequency.