Full waveform inversion (FWI) is a high resolution inversion method，which can reveal detailed in- formation of the structure and lithology under complex geological background． It is limited by many kinds of noi- ses when the method applied to the real seismic data． Based on Huber function criterion，the objective function combinates the anti- noise of L 1 norm and the stability of L 2 norm in theory，the authors derive the gradient for- mula of the Huber function by using L- BFGS algorithm for FWI． The new method is proved by synthetic seismic data with the Gaussian noise and the impulse noise． Numerical test results show that L- BFGS algorithm is ap- plied to the frequency domain FWI with the convergence speed and high calculation accuracy，and can effec- tively reduce computer memory usage; and the Huber function is more robust and stable than L 2 norm even with the noises．