Electromagnetic bandgap (EBG) microstrip structures have been proposed in the application of antenna and microwave filter design. This thesis demonstrates a design procedure for the EBG structure to achieve a wide stopband low-pass filter, by combining tapered etched holes and multi-period EBG structure. The measurement result shows the refection band is from 6.8 GHz to 25 GHz, which meets the simulation result. Then we use Genetic Algorithms (GA) to optimize the placement of structures that meets the desired specification. A low-pass filter is fabricated and measured. The theoretical and experimental performance shows good agreement, therefore proves the functionality of this method.