The specific heat of the recently discovered superconductor MgB2 has been measured at temperatures rangingfrom 4.5 to 80K. The superconducting anomaly △C at Tc is clearly observed. The total specific heat in thenormal state can be well fitted by electronic and phonon contributions. The Debye temperature θD is found to be737K, much larger than other intermetallic superconductors. The normal-state electronic specific heat coefficientγ is found to be 2.48±0.5 mJ/mol. K2 and △C/γTc is between 1.41 and 2.15.