A novel dual-band electromagnetic bandgap (EBG) for wireless local area network (WLAN) applications is designed in this paper. The EBG structure is based on hexagonal geometry and does not use via or multilayer. The bandgap characteristics are investigated by determining the scatter parameters. By adjusting the parameters in the dimension of the structure, the dual bandgaps can be controlled easily to achieve the WLAN frequencies. Comparisons between the proposed structure with another one, which have the same dielectric permittivity and thickness of the dielectric substrate, have been done. The structure is then also optimized to obtain the high impedance in surface at the frequencies of the WLAN bands, which are centered at 2.45 GHz and 5.5 GHz. Simulated and measured results are shown to demonstrate the performance of the proposed structure.