A compact CPW-fed double T-Shaped antenna is proposed for dual-band wireless local area network (WLAN) operations. For the proposed antenna, the -10 dB return loss bandwidth could reach about 25.5% for the 2.4 GHz band and 5.7 % for the 5 GHz band, which meet the required bandwidth specification of WLAN standard. To reduce the mutual coupling and get high isolation between two dual-band antennas, we proposed the novel electromagnetic band gap (EBG) structures. When the EBG structure is employed, a -13dB and -30dB mutual coupling reduction is achieved at 2.4 and 5.2 GHz. It shows that the features of small size, uniplanar structure, good radiation characteristics and small mutual coupling are promising for multi-input multi-output (MIMO) applications.