A compact UWB-MIMO antenna design with an impedance bandwith from 3.2 GHz to 9.1 GHz is presented. The MIMO antenna has a transmission coefficient response less than -14 dB at the resonance frequency bandwidth. To improve the isolation and the antenna performance, an Electromagnetic Band Gap (EBG) structure is introduced between elements, that consists of an added microstrip at ground plane, a 9x1 periodic metal-square patches on top of the substrate, and vertical vias connecting the patches to the ground plane. The EBG structure design methodology is presented. The isolation enhancement between elements is 4 dB at frequency bandwidth. The compact UWB-MIMO antenna with EBG structure reaches a maximum isolation of -33 dB at 6.42 GHz. The peak gain is 4.8 dBi at 7.3 GHz in the H-plane radiation, and 3.3 dBi at 7.3 GHz in the E-plane radiation.