In this paper,an Enhanced Self-Attention (ESA) mechanism has been put forward for robust feature extraction.The proposed ESA is integrated with the recursive gated convolution and self-attention mechanism.In particular, the former is used to capture multi-order feature interaction and the latter is for global feature extraction.In addition, the location of interest that is suitable for inserting the ESA is also worth being explored.In this paper, the ESA is embedded into the encoder layer of the Transformer network for automatic speech recognition (ASR) tasks, and this newly proposed model is named GNCformer. The effectiveness of the GNCformer has been validated using two datasets, that are Aishell-1 and HKUST.Experimental results show that, compared with the Transformer network,0.8%CER,and 1.2%CER improvement for these two mentioned datasets, respectively, can be achieved.It is worth mentioning that only 1.4M additional parameters have been involved in our proposed GNCformer.