Software developers frequently use code completion tools to accelerate software development by suggesting the following code elements. Researchers usually employ AutoRegressive (AR) decoders to complete code sequences in a left-to-right, token-by-token fashion. To improve the accuracy and efficiency of code completion, we argue that tokens within a code statement have the potential to be predicted concurrently. In this paper, we first conduct an empirical study to analyze the dependency among the target tokens in line-level code completion. The results suggest that it is potentially practical to generate all statement tokens in parallel. To this end, we introduce SANAR, a simple and effective syntax-aware non-autoregressive model for line-level code completion. To further improve the quality of the generated code, we propose an adaptive and syntax-aware sampling strategy to boost the model’s performance. The experimental results obtained from two widely used datasets indicate that our model outperforms state-of-the-art code completion approaches of similar model size by a considerable margin, and is faster than these models with up to 9 × speed-up. Moreover, the extensive results additionally demonstrate that the enhancements achieved by SANAR become even more pronounced with larger model sizes, highlighting their significance.