Blind source separation is aimed at recovering original independent signals when their linear mixtures are observed. Various methods for estimating a recovering matrix have been proposed and applied to data in many fields, such as biological signal processing, communication engineering, and financial market data analysis. One problem these methods have is that they are often too sensitive to outliers, and the existence of a few outliers might change the estimate drastically. In this article, we propose a robust method of blind source separation based on theβ divergence. Shift parameters are explicitly included in our model instead of the conventional way which assumes that original signals have zero mean. The estimator gives smaller weights to possible outliers so that their influence on the estimate is weakened. Simulation results show that the proposed estimator significantly improves the performance over the existing methods when outliers exist; it keeps equal performance otherwise.