The high-fluence GRB131108A at redshift z=2.4, was detected by the Mini-Calorimeter (MCAL, 0.35-100 MeV) and the Gamma- Ray Imaging Detector (GRID, 30 MeV - 30 GeV) onboard the AGILE satellite. The burst emission consisted of a very bright initial peak,lasting 0.1 s, followed by a fainter emission detected for ~25 s with the MCAL and ~80 s with the GRID. The AGILE spectra, when compared with those reported at lower energies, indicate the presence of a prominent high-energy component with peak energy in the 10-20 MeV region. Contrary to other GRBs, this high-energy component is present also during the initial peak, with power law photon index of about -1.6 below 10 MeV and -2.35+-0.2 above 30 MeV.