Polycrystalline samples of the new superconductor MgB2 are prepared by a solid-state reaction using Mg and Bpowders. The resistance measurement shows that the onset transition temperature and zero resistance transitiontemperature are Tonsetc = 43.8 K and Tc0 = 37 K, respectively. The Tco strongly depends on measuring current. The diamagnetic transition temperature of ～38 K is obtained by the ac susceptibility measurement. X-ray powderdiffraction spectra of MgB2 can be indexed using hexagonal structure with space group P6/mmm and latticeparameters a = 0.30864 and c = 0.35212 nm. A second phase, probably MgO, is also found.