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Utilizing the opposite phase shifting property of a standard Composite Right/Left Handed (CRLH) transmission line (TL) and a dual structure of CRLH (D-CRLH) TL, a dual-band balun is designed. The dual-band balun is formed by a 1x2 (3-dB) splitter with a D-CRLH phase-shifting line in the top branch and a CRLH phase-shifting line in the bottom branch. The performance of the balun is verified with circuit simulation at 2.4 GHz and 5.0 GHz. The balun exhibits a very wide bandwidth for differential output phase, the return loss is well below -100 dB, and the insertion losses |S12| and |S13| are -3.03 plusmn 0.05 dB at both frequencies.