Clustering is a fundamental problem in unsupervisedlearning. Popular methods like K-means,may suffer from instability as they are prone toget stuck in its local minima. Recently, the sumof-norms(SON) model (also known as clusteringpath), which is a convex relaxation of hierarchicalclustering model, has been proposed in(Lindsten et al., 2011) and (Hocking et al., 2011).Although numerical algorithms like alternatingdirection method of multipliers (ADMM) and alternatingminimization algorithm (AMA) havebeen proposed to solve convex clustering model(Chi & Lange, 2015), it is known to be very challengingto solve large-scale problems. In this paper,we propose a semismooth Newton based augmentedLagrangian method for large-scale convexclustering problems. Extensive numerical experimentson both simulated and real data demonstratethat our algorithm is highly efficient androbust for solving large-scale problems. Moreover,the numerical results also show the superiorperformance and scalability of our algorithm comparingto existing first-order methods.