This paper proposes an efficient memory transformer Emformer for low latency streaming speech recognition. In Emformer, the long-range history context is distilled into an augmented memory bank to reduce self-attention's computation complexity. A cache mechanism saves the computation for the key and value in self-attention for the left context. Emformer applies a parallelized block processing in training to support low latency models. We carry out experiments on benchmark LibriSpeech data. Under average latency of 960 ms, Emformer gets WER $2.50\%$ on test-clean and $5.62\%$ on test-other. Comparing with a strong baseline augmented memory transformer (AM-TRF), Emformer gets $4.6$ folds training speedup and $18\%$ relative real-time factor (RTF) reduction in decoding with relative WER reduction $17\%$ on test-clean and $9\%$ on test-other. For a low latency scenario with an average latency of 80 ms, Emformer achieves WER $3.01\%$ on test-clean and $7.09\%$ on test-other. Comparing with the LSTM baseline with the same latency and model size, Emformer gets relative WER reduction $9\%$ and $16\%$ on test-clean and test-other, respectively.