Liu, Y., Zhang, J. and Hu, G., 2014. Variable step size-normalized sign gradient AVO inversion algorithm. Journal of Seismic Exploration, 23: 265-278. Pre-stack seismic inversion faces difficulties when applied to real seismic data because of the existence of many types of noise. As we know, the /, norm minimization gives more robust solutions than the /, norm does because it is less sensitive to spiky and high-amplitude noise. To take advantage of /, norm and constraint on the deviation between two adjacent solutions, a variable step size-normalized sign gradient algorithm (VSS-NSGA) is proposed to obtain a more rational inversion result. By minimizing the An norm of the error vector with a minimum disturbance constraint, the proposed VSS-NSGA not only reduces the computational cost of the large scale seismic inversion problems but also avoids the instability of the /, norm solution using the iteratively reweighted least squares (IRLS) algorithm. Furthermore, the variable step size is introduced to overcome the contradiction of the fast convergence rate and small steady-state error brought by fixed step size. Synthetic tests demonstrate that the proposed VSS-NSGA algorithm out-performs the traditional IRLS method in both convergence rate and steady-state error. The real data example shows the validity of the proposed method for AVO inversion.