Seismic full waveform inversion (FWI) has been highly challenging due to the inherent nonlinearity, non-uniqueness and illposedness. Generally, various regularization methods are required to obtain a stable solution. We have developed a new adaptive edge-preserving regularization scheme for FWI. The salient features of our algorithm include an efficient approach to constrain the sharp interfaces of the model discontinuities through the total variation (TV) regularization and a novel approach to adaptively compute the regularization parameter. TV regularization accomplishes these goals by imposing the sparsity on the gradients of the model parameters. The inversion relies on a classic iterative steepest descent algorithm in the frequency domain by proceeding a group of frequencies from lower to higher ones. We adopt the adaptive method to estimate the regularization parameter. Hence, we can save much running time for the inversion. The test on the SEG/EAGE Overthrust model shows that the proposed method is able to produce a better model and a better data fit compared to the second-order Tikhonov regularization method.