The refraction index of the quantized lossy composite right-left handed transmission line (CRLH-TL) is deduced in the thermal coherence state.The results show that the negative refraction index (herein the left-handedness) can be implemented by the electric circuit dissipative factors(i.e.,the resistances R and conductances G) in a higher frequency band (1.446 GHz≤ ω ≤ 15 GHz),and flexibly adjusted by the left-handed circuit components (C1,L1) and the right-handed circuit components (Cr,Lr) at a lower frequency (ω =0.995 GHz).The flexible adjustment for left-handedness in a wider bandwidth will be significant for the microscale circuit design of the CRLH-TL and may make the theoretical preparation for its compact applications.