Single crystals of magnesium diboride (MgB2) have been grown at ambient pressure by using Mg-self-flux method. We chose the marketed MgB2 powder as the raw material and Mg as the flux. The temperature was raised from room temperature to 1035degreesC for 4 h and maintained so for 2 h and then cooled down to room temperature slowly and then the single crystals of MgB2 with hexagonal shape and a superconducting transition at about 37 K were obtained. The Xray powder diffraction confirmed the MgB2 phase, scanning electron microscope observed the single crystal images and electron diffraction patterns by using high-resolution transmission electron microscope confirmed the structure of MgB2 single crystal. A new mechanism of liquid-assisted solid-state re-crystallization for growth of MgB2 single crystal is proposed. (C) 2004 Elsevier B.V. All rights reserved.