Nonnegative matrix factorization seeks to find a basic matrix and a weight matrix to approximate the nonnegative matrix. It has proven to be a powerful low-rank decomposition technique for nonnegative multivariate data. However, its performance largely depends on the assumption of a fixed number of features. In this work, we propose a new probabilistic nonnegative matrix factorization which factorizes a nonnegative matrix into a low-rank factor matrix with {0,1} constraints and a nonnegative weight matrix. In order to automatically learn the potential binary features and feature number. A deterministic Indian buffet process variational inference is introduced to obtain the binary factor matrix. And the weight matrix is set to satisfy the exponential prior. In order to obtain the real posterior distribution of the two factor matrices, a variational Bayesian exponential Gaussian inference model is established. The comparative experiments on both the synthetic and real-world data sets show the efficacy of the proposed method.