In this work, we focus on a deep structure-enforced nonnegative matrix factorization (DSeNMF) which represents a large class of deep learning models appearing in many applications, especially sparsity-constrained deep NMF. We present a unified algorithm framework, based on the classic alternating direction method of multipliers (ADMM). For updating subproblems, we derive an efficient updating rule according to its KKT conditions. We compare the proposed algorithm with state-of-the-art deep semi-NMF on MNIST dataset. Results show that our algorithm performs better and the deep model indeed obtain a better clustering accuracy than the single-layer model. In addition, the deep model and algorithm provide flexible and potential applicability for data representation.