A novel compact, planar, and coplanar waveguide (CPW)-fed dual-band antenna is designed and proposed using composite metamaterial. Such composite metamaterial consists of an inner split-ring resonator (SRR) and an outer closed-ring resonator (CRR). The composite metamaterial can provide dual-band operation at 2.595–2.654 and 3.185–4.245 GHz with reflection coefficient better than $-$10 dB by the two resonant modes of SRR and CRR, respectively. A CPW-fed line with trapeziform ground plane and tapered impedance transformer line is employed to improve the impedance matching of the antenna. The uniqueness of this design is that the inner SRR with size much smaller than the resonant wavelength is used for obtaining the lower narrow frequency band, which makes the dual-band antenna very compact. Antenna parameters, including reflection coefficient, radiation pattern, radiation efficiency, and gain, are analyzed with numerical simulation and experimental measurement. Good agreement between the simulation and measurement is observed.