In this paper, an on-line nonnegative matrix factorization (NMF) algorithm for acoustic signal processing systems is developed based on the recursive least squares (RLS) method. In order to develop the on-line NMF algorithm, we reformulate the NMF problem into multiple least squares (LS) normal equations, and solve the reformulated problems using RLS methods. In addition, we eliminate the irrelevant calculations based on the NMF model. The proposed algorithm has been evaluated with a well-known dataset used for NMF performance evaluation and with real acoustic signals; the results show that the proposed algorithm performs better than the conventional algorithm in on-line applications.