The Glasso applied to portfolio selection achieves significant risk reduction and boosts certainty-equivalent returns (CER) in high dimensions through sparse estimation against hedge trades (Goto and Xu, 2015). However, the sample covariance matrix used as input for the Glasso analysis is susceptible to data outliers. This input is replaced in our Glasso by a Kendall-type robust estimator (Glasso-K). Such new robust Glasso inherits the original Glasso's risk reduction advantage while dealing well with data contamination. The Glasso-K is found to outperform the Glasso in main aspects, especially in the CER due to its induced better-conditioned covariance, less-frequent turnover, and more-diversified portfolios. The robust Glasso also performs better than many non-Glasso strategies well established in the literature, and its superior performance consists in complete removal of sample means from covariance estimation.