An unconditionally stable finite-difference time-domain method to analyse the composite right/left handed (CRLH) transmission lines (TLs) is proposed. The conventional algorithm presented to analyse the CRLH TLs is not capable of analysing special case of the CRLH TLs such as pure left-handed TLs due to numerical stability problem. The proposed unconditionally stable algorithm removes the numerical instability and can analyse all the CRLH and pure left-handed TLs. Amplification matrix of the proposed algorithm is calculated and numerical stability of the presented algorithm is studied. The proposed algorithm is applied to some examples and results are verified by the results of the conventional algorithm and results of Agilent ADS software. The results indicate that the CPU time of the proposed algorithm is reduced about 99% than that of the conventional algorithm by using the complex phasor method and unconditionally stable algorithm.