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End-to-end speech recognition has become popular in recent years, since it can integrate the acoustic, pronunciation and language models into a single neural network. Among end-to-end approaches, attention-based methods have emerged as being superior. For example, Transformer, which adopts an encoder-decoder architecture. The key improvement introduced by Transformer is the utilization of self-attention instead of recurrent mechanisms, enabling both encoder and decoder to capture long-range dependencies with lower computational complexity.In this work, we propose boosting the self-attention ability with a DFSMN memory block, forming the proposed memory equipped self-attention (SAN-M) mechanism. Theoretical and empirical comparisons have been made to demonstrate the relevancy and complementarity between self-attention and the DFSMN memory block. Furthermore, the proposed SAN-M provides an efficient mechanism to integrate these two modules. We have evaluated our approach on the public AISHELL-1 benchmark and an industrial-level 20,000-hour Mandarin speech recognition task. On both tasks, SAN-M systems achieved much better performance than the self-attention based Transformer baseline system. Specially, it can achieve a CER of 6.46% on the AISHELL-1 task even without using any external LM, comfortably outperforming other state-of-the-art systems.