In this paper, a mathematical design for dual-band matching of arbitrary impedances is presented based on Composite Right/Left Handedness (CRLH) and conventional transmission line theories. This design process of transforming arbitrary impedances to 50 ohms at two frequencies suggests an analytic approach to dual-band matching for multi-band devices. As well, bandwidth analysis of the proposed method is presented for wideband applications. For the verification, CRLH transmission lines were built successfully to match the output impedances of a commercial transistor at 824MHz and 2.5GHz. This work is expected to be useful for the extraction of general solutions for the dual-band matching network of arbitrary impedances.