A key problem in level set tracking is to construct a discriminative speed function for effective contour evolution. In this paper, we propose a level set tracking method based on a discriminative speed function, which produces a superpixel-driven force for effective level set evolution. Based on kernel density estimation and metric learning, the speed function is capable of effectively encoding the discriminative information on object appearance within a feasible metric space. Furthermore, we introduce adaptive object shape modeling into the level set evolution process, which leads to the tracking robustness in complex scenarios. To ensure the efficiency of adaptive object shape modeling, we develop a simple but efficient weighted non-negative matrix factorization method that can online learn an object shape dictionary. Experimental results on a number of challenging video sequences demonstrate the effectiveness and robustness of the proposed tracking method.