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We report the specific heat measurements on the newly discovered Fe-based layered LaO0.9F0.1-δFeAs supercon-ductor with the onset transition temperature Tc≈28 K. A nonlinear magnetic field dependence of the electronic specific heat coefficient γ(H) has been found in the low temperature limit, which is consistent with the prediction for a nodal superconductor. The maximum gap value △0 ≈ 3.4 ± 0.5 me V is derived by analysing γ( H) based on the d-wave model. We also detected the electronic specific heat difference between 9 T and 0 T in a wide temper-ature range, a specific heat anomaly can be clearly observed near Tc. The Debye temperature of our sample is determined to be about 315.7K. Our results suggest an unconventional mechanism for this new superconductor.