Turning attention to a particular speaker when many people talk simultaneously is known as the cocktail party problem. It is still a tough task that remained to be solved especially for singlechannel speech separation. Inspired by the physiological phenomenon that humans tend to distinguish some attractive sounds from mixed signals, we propose the multi-head self-attention deep clustering network (ADCNet) for this problem. We creatively combine the widely used deep clustering network with multihead self-attention mechanism and exploit how the number of heads in multi-head self-attention affects separation performance. We also adopt the density-based canopy K-means algorithm to further improve performance. We trained and evaluated our system using the Wall Street Journal dataset (WSJ0) on two and three talker mixtures. Experimental results show the new approach can achieve a better performance compared with many advanced models.