We demonstrate a method to create a high Q factor two-dimensional (2D) electromagnetic band gap (EBG) structure with composite defects in center of the structures. By theoretical calculation, we show that a single-mode 2D EBG structure can be created by composite defect EBG structure. Meantime, high Q factor and single mode can be acquired. The dispersion relations and impedance in the slow wave structures based on EBG are simulated compared to the parameters in traditional structures. These results provide very important guidelines for designing of the 2D EBG structure which can be used in traveling-wave tube device.