In computer vision tasks, it frequently happens that gross noise occupies the absolute majority of the data. Most robust estimators can tolerate no more than 50% gross errors. In this article, we propose a highly robust estimator, called MDPE (Maximum Density Power Estimator), employing density estimation and density gradient estimation techniques in the residual space. This estimator can tolerate more than 85% outliers. Experiments illustrate that the MDPE has a higher breakdown point and less errors than other recently proposed similar estimators: Least Median of Squares (LMedS), Residual Consensus (RESC), and Adaptive Least kth Order Squares(ALKS).