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We use a lirst-principles plane wave method with the new relativistic analytic pseudopotential of the Hartwigsen,Goedecker and Hutter (HGH) scheme and the pseudopotential of the Troullier Martins scheme to calculate the electron-phonon coupling constant λ of superconducting MgB2. The calculated results show that there is a peak at about 300-350 cm-1 in the electron-phonon spectral functional α2 F(ω), duo to the coupling of the electrons to the acoustic phonon, and the relativistic effect appears in the high frequencies zone. All the results agree well with the present and previous experimental data.