In this paper, the audio blind source separation (BSS) using three dimensional Nonnegative Tensor Factorization (3D-NTF), is realized. The audio source separation is modeled as an optimization problem and the P-divergence cost function is iteratively optimized by alternating multiplicative update rules. The traditional measures which are used to evaluate the decomposition performance are known to be not informative about perceptual quality of the audio signals. Therefore performance of the designed system is evaluated not only with the well known Amari index, but also with perceptual audio quality criterions which are defined in the recommendation report, ITU-R BS.1387 of International Telecommunication Union (ITU). In this study, it has been shown that source decompositon performance of the NTF modelling on audio data mixed under different conditions, is superior to the Nonnegative Matrix Factorization (NMF). Furthermore, it has been observed that some of the decomposed sources are acceptable according to Amari index while thay are not with respect to the perceptual quality citeria thus it can be concluded that the perceptual criteria is more suitable to objective quality evaluation of audio.