We have measured the Raman spectra of polycrystalline MgB 2 from 25 cm −1 to 1200 cm −1 . When the temperature was decreased below the superconducting transition temperature T c , we observed a superconductivityinduced redistribution in the electronic Raman continuum. Two pair-breaking peaks appear in the spectra, suggesting the presence of two superconducting gaps. Furthermore, we have analyzed the measured spectra using a quasi twodimensional model in which two s-wave superconducting gaps open on two sheets of Fermi surface. For the gap values we have obtained ∆ 1 = 22cm −1 (2.7 meV) and ∆ 2 = 50cm −1 (6.2 meV). Our results suggest that a conventional phonon-mediated pairing mechanism occurs in the planar boron σ bands and is responsible for the superconductivity of MgB 2 .