Recently, sparsity based classification has been applied to video anomaly detection. A linear model is assumed over video features (e.g. trajectories) such that the feature representation of a new event is written as a sparse linear combination of existing feature representations in the dictionary. Sparsity based video anomaly detection shows promise but open challenges remain in that existing methods assume object specific and class specific event dictionaries making them applicable mostly in highly structured scenarios. Second, using conventional sparsity models on matrices/vectors, the computational burden is often high. In this work, we advocate a more general and practical sparsity model using a low-rank structure on the matrix of sparse coefficients. We find that enforcing a low-rank structure can ease the rigidity of traditional row-sparse constraints on sparse coefficient vectors/matrices. Because low-rank matrices are of course not always sparse, an additional l1 regularization term is added. Further, if rank is substituted by its convex nuclear norm alternative, then significant computational benefits can be obtained over existing methods in sparsity based video anomaly detection. Experimental evaluation on benchmark video datasets reveal, our method is competitive with state-of-the art while providing robustness benefits under occlusion.