Clustering is an unsupervised learning approach that explores data and seeks groups of similar objects. Many classical clustering models such as k-means and DBSCAN are based on heuristics algorithms and suffer from local optimal solutions and numerical instability. Recently convex clustering has received increasing attentions, which leverages the sparsity inducing norms and enjoys many attractive theoretical properties. However, convex clustering is based on Euclidean distance and is thus not robust against outlier features. Since the outlier features are very common especially when dimensionality is high, the vulnerability has greatly limited the applicability of convex clustering to analyze many real-world datasets. We address the challenge by proposing a novel robust convex clustering method that simultaneously performs convex clustering and identifies outlier features. Specifically, the proposed method learns to decompose the data matrix into a clustering structure component and a group sparse component that captures feature outliers. We develop a block coordinate descent algorithm which iteratively performs convex clustering after outliers features are identified and eliminated. We also propose an efficient algorithm for solving the convex clustering by exploiting the structures on its dual problem. This is the code for the proposed method. Folder examples shows the efficiency comparision of our method and AMA on solving convex clustering problem and how robust convex clustering detect outlier features.