In this paper, a decomposition method is proposed for Separable Non-negative Tensor Factorization (SNTF), which yields a structure similar to the PARATUCK2 model for the decomposition of non-negative tensors. Among many different possibilities for performing tensor factorization, we develop a specific procedure for SNTF with an aim to decompose multi-way dataset expressed in the form of a tensor into low-rank components that extract dominant features in the data. The SNTF method is evaluated using real image data and the results show that the proposed SNTF is superior to other NTF methods in terms of error performance and computational efficiency.