PSR J1513-5908 is a young energetic pulsar which exhibits a hard power-law like spectrum in the hard X-ray band (10-300 keV) with a peak energy (in nu F nu) at a few MeV. We present the broad-band SED and pulse profiles from keV to GeV energies, exploiting the 30-100 MeV capabilities of the Fermi LAT, and discuss possible emission mechanisms responsible for its remarkable spectrum.