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Lipreading is an impressive technique and there has been a definite improvement of accuracy in recent years. However, existing methods for lipreading mainly build on autoregressive (AR) model, which generate target tokens one by one and suffer from high inference latency. To breakthrough this constraint, we propose FastLR, a non-autoregressive (NAR) lipreading model which generates all target tokens simultaneously. NAR lipreading is a challenging task that has many difficulties: 1) the discrepancy of sequence lengths between source and target makes it difficult to estimate the length of the output sequence; 2) the conditionally independent behavior of NAR generation lacks the correlation across time which leads to a poor approximation of target distribution; 3) the feature representation ability of encoder can be weak due to lack of effective alignment mechanism; and 4) the removal of AR language model exacerbates the inherent ambiguity problem of lipreading. Thus, in this paper, we introduce three methods to reduce the gap between FastLR and AR model: 1) to address challenges 1 and 2, we leverage integrate-and-fire (I\&F) module to model the correspondence between source video frames and output text sequence. 2) To tackle challenge 3, we add an auxiliary connectionist temporal classification (CTC) decoder to the top of the encoder and optimize it with extra CTC loss. We also add an auxiliary autoregressive decoder to help the feature extraction of encoder. 3) To overcome challenge 4, we propose a novel Noisy Parallel Decoding (NPD) for I\&F and bring Byte-Pair Encoding (BPE) into lipreading. Our experiments exhibit that FastLR achieves the speedup up to 10.97$\times$ comparing with state-of-the-art lipreading model with slight WER absolute increase of 1.5\% and 5.5\% on GRID and LRS2 lipreading datasets respectively, which demonstrates the effectiveness of our proposed method.