The structural features of MgB2 superconductors prepared under different conditions have been analysed by means of transmission electron microscopy. The MgB2 crystal is identified to have a hexagonal structure with the space group of P6/mmm. Superconducting materials synthesized under a high pressure of 6 Gpa are made of regularly stacked grains as large as a few microns in sizes. Stacking faults and microstructure properties of grain boundaries, either with or without impurities, appearing in a sample with the critical current density greater than l05A/cm2, have been systematically investigated.