Contemporary recommendation systems are designed to meet users' needs by delivering tailored lists of items that align with their specific demands or interests. In a multi-stage recommendation system, reranking plays a crucial role by modeling the intra-list correlations among items. The key challenge of reranking lies in the exploration of optimal sequences within the combinatorial space of permutations. Recent research proposes a generator-evaluator learning paradigm, where the generator generates multiple feasible sequences and the evaluator picks out the best sequence based on the estimated listwise score. The generator is of vital importance, and generative models are well-suited for the generator function. Current generative models employ an autoregressive strategy for sequence generation. However, deploying autoregressive models in real-time industrial systems is challenging. To address these issues, we propose a Non-AutoRegressive generative model for reranking Recommendation (NAR4Rec) designed to enhance efficiency and effectiveness. To tackle challenges such as sparse training samples and dynamic candidates, we introduce a matching model. Considering the diverse nature of user feedback, we employ a sequence-level unlikelihood training objective to differentiate feasible sequences from unfeasible ones. Additionally, to overcome the lack of dependency modeling in non-autoregressive models regarding target items, we introduce contrastive decoding to capture correlations among these items. Extensive offline experiments validate the superior performance of NAR4Rec over state-of-the-art reranking methods. Online A/B tests reveal that NAR4Rec significantly enhances the user experience. Furthermore, NAR4Rec has been fully deployed in a popular video app Kuaishou with over 300 million daily active users.