An optimally doped iron-based superconductor LaFeAsO_0.92F_0.08 with T_c = 29 K has been studied by inelastic powder neutron scattering. The magnetic excitation at Q=1.15 Å^-1 is enhanced below T_c, leading to a peak at E_res∼13 meV as the resonance mode, in addition to the formation of a gap at low energy below the crossover energy Δ_c∼10 meV. The peak energy at Q=1.15 Å^-1 corresponds to 5.2 k_B T_c in good agreement with the other values of resonance mode observed in the various iron-based

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... perconductors, even in the high-T_c cuprates. Although the phonon density of states has a peak at the same energy as the resonance mode in the present superconductor, the Q-dependence is consistent with the resonance being of predominately magnetic origin.