The self-attention architecture is also considered to be a significant contribution in sequence processing tasks. It has the ability to highlight the distinctive features of a sequence, has been very successful in natural language processing and speech separation. In addition, the intra- and inter-architecture of the dual-path bi-directional long-short term memory framework has been demonstrated to be very effective for processing extremely long sequences. Based on these properties, we design a core architecture called intra- and inter-self-attention framework. Parallel models is more efficient and stable than a single model. In this research, we propose a parallel intra- and inter-self-attention framework (PI2SA) for the cocktail party effect task. The experimental results demonstrate that our PI2SA is remarkably effective. It outperforms both traditional self-attention models and a basic intra- and inter-architecture. Our PI2SA achieves competitive results with state-of-the-art deep learning models on the cocktail party effect problem.