The research for coplanar-waveguide transmission line has become an important project recently due to its advantages such as low profile, light weight and low cost. Meanwhile, along with the requirement of developing the communication equipment into a mult-functional and miniaturized one, dual-band antenna also attracts more attention. In this paper, a CPW-fed dual-band antenna is proposed, and the working principle of it is analyzed, consequently, the relation between working frequency and geometry sizes is obtained. And then, some key techniques and notes about FDTD are introduced, such as the setting of source, modified technique of near-field to far-field and setting of radiation boundary. Compared to traditional setting source, adopting mode match method can decrease the computation time. Finally, the computed results by FDTD and measured results are given, both of which have a good agreement at the working band. It has guidance meaning to design this kind of dual-band antenna, according to dual-band mechanism proved by electric field distribution. At the same time, the working mechanism of the dual-band is demonstrated by electric field distribution, which shows a guidance meaning to the parameter selection in the design of this kind of dual-band antenna.