We report the spectral analysis of the X-ray pulsar LMC X–4 in its high state out of eclipse observed by BeppoSAX . During this observation no coherent pulsations are detected . The primary continuum is well described by a power law with a high energy cutoff ( E _ { cutoff } \sim E _ { fold } \sim 18 keV ) . The addition of a cyclotron absorption line at \sim 100 keV improves the fit significantly . The inferred magnetic moment is 1.1 \times 10 ^ { 31 } Gauss cm ^ { 3 } , in agreement with the value estimated assuming that the neutron star is at the spin equilibrium , as it has been proposed for this source . The remaining excess at low energies can be fitted by a Comptonization of soft photons by moderately hot electrons ( kT \sim 0.9 keV ) , with an optical depth \tau \sim 16 . The seed photons for this Comptonization are consistent with black body emission from the accretion disk at the magnetospheric radius . Another possibility is to fit the soft excess with black body and thermal bremsstrahlung . In this case the black body would originate from cold plasma at the magnetosphere while the bremsstrahlung component may be produced by the strong stellar wind from the companion star , ionized by the X-ray emission from the pulsar .