On-line portfolio selection has been attracting increasing interests from artificial intelligence community in recent decades. Mean reversion, as one most frequent pattern in financial markets, plays an important role in some state-of-the-art strategies. Though successful in certain datasets, existing mean reversion strategies do not fully consider noises and outliers in the data, leading to estimation error and thus non-optimal portfolios, which results in poor performance in practice. To overcome the limitation, we propose to exploit the reversion phenomenon by robust L1-median estimator, and design a novel on-line portfolio selection strategy named "Robust Median Reversion" (RMR), which makes optimal portfolios based on the improved reversion estimation. Empirical results on various real markets show that RMR can overcome the drawbacks of existing mean reversion algorithms and achieve significantly better results. Finally, RMR runs in linear time, and thus is suitable for large-scale trading applications.