Non-negative sparse coding (NSC) is a powerful technique for low-rank data approximation, and has found several successful applications in signal processing. However, the temporal dependency, which is a vital clue for many realistic signals, has not been taken into account in its conventional model. In this paper, we propose a general framework, i.e., convolutive non-negative sparse coding (CNSC), by considering a convolutive model for the low-rank approximation of the original data. Using this model, we have developed an effective learning algorithm based on the multiplicative adaptation of the reconstruction error function defined by the squared Euclidean distance. The proposed algorithm is applied to the separation of music audio objects in the magnitude spectrum domain. Interesting numerical results are provided to demonstrate its advantages over both the conventional NSC and an existing convolutive coding method.