Enlightened by the success of machine learning techniques in various application areas, recent years have witnessed a surge of research efforts on automatic program repair (APR) using machine learning techniques. Previous machine learning-based APR techniques essentially modified bugs in the autoregressive (AR) manner, which predicts future values based on past values. Due to the manner of token-by-token generation, the AR-based APR technique has a huge time delay. In particular, the delay of the APR model with a large number of parameters is more serious. To address the issue, we aim to apply the non-autoregressive (NAR) method to the APR task, which can output target code in a parallel manner to avoid huge repair delays. However, the naive use of the NAR manner for the APR task suffers from the issue of compromised patch quality. To effectively adapt the NAR manner for the APR task, we in this paper propose NARRepair, the first customized NAR code generation model for the APR task. The NARRepair model features three major novelties, including 1) the repair action predictor for alleviating the over-correction issue, 2) the inter-token dependency extractor for alleviating the issue of lacking inter-token dependency information, and 3) the two-stage decoder for alleviating the issue of lacking contextual information. We evaluated NARRepair on three widely used datasets in the APR community, and the results show that 1) compared to other APR techniques, the NARRepair model has the best performance within the limited repair time, and 2) compared to AR-based APR techniques, the repair speed of NARRepair has been increased by 1.4-6.4 times in the GPU environment. Overall, the results show that NARRepair has achieved state-of-the-art comprehensive performance in terms of repair speed and accuracy.