Low energy spin fluctuations are studied for the electron-doped Fe-based superconductor LaFeAsO(1-x)F(x) by inelastic neutron scattering up to the energy transfer of w = 15 meV using polycrystalline samples. Superconducting samples (x=0.057, Tc=25 K and x=0.082, Tc=29 K) show dynamical spin susceptibility chi(w) almost comparable with the parent samples. However chi(w) is almost vanished in the x=0.158 sample where the superconductivity is highly suppressed. These results are compatible with the theoretical suggestions that the spin fluctuation plays an important role for the superconductivity.