Full waveform inversion( FWI) is a high resolution inversion method,which can reveal detailed information of the structure and lithology under complex geological background. It is limited by many kinds of noises when the method applied to the real seismic data. Based on Huber function criterion,the objective function combinates the anti-noise of L1 norm and the stability of L2 norm in theory,the authors derive the gradient formula 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 applied to the frequency domain FWI with the convergence speed and high calculation accuracy,and can effectively reduce computer memory usage; and the Huber function is more robust and stable than L2 norm even with the noises. Full waveform inversion (FWI) is a high resolution inversion method, which can reveal detailed information of the structure and lithology under complex geological background. It is limited by many kinds of noises when the method applied to the real seismic data. It is based on Huber function criterion, the objective function combinates the anti-noise of L1 norm and the stability of L2 norm in theory, the authors derive the gradient formula 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 applied to the frequency domain FWI with the convergence speed and high calculation accuracy, and can effectively reduce computer memory usage; and the Huber function is more robust and stable than L2 norm even with the noises.