The presented EBG structure covers WiFi-2.4/5.2/5.8 GHz bands. The EBG structure is used to improve isolation and to reduce distance between antennas in a MIMO antenna system of a wireless router. The size of the presented 4x4 MIMO antennas is 87.6x87.6x3.2 mm^3. Those antennas are very low profile.This technique presented the MIMO antennas combined a EBG structure. Therefore, the isolation between antennas improves and the distance between antenna reduces. The area of the single antenna is 43.8 x 43.8 mm^2(~0.35 wavelength@2.4 GHz). The MIMO antennas can be combined arbitrary as a 2x2, 4x4,...MIMO antennas system by the single antenna. The MIMO antenna system can be mounted any walls or metal surfaces, because of the EBG structure behind the MIMO antenna.The MIMO antennas places before the EBG structure. The overall thickness is 3.2 mm. The radiation pattern of the MIMO antennas, which covers whole WLAN bnads, is directional. Therefore, this MIMO antenna can be used in wireless router. The MIMO antenna can be mounted on any walls and metal surface because of the EBG structure behind the MIMO antenna.