Reranking plays a crucial role in modern multi-stage recommender systems by rearranging the initial ranking list. Due to the inherent challenges of combinatorial search spaces, some current research adopts an evaluator-generator paradigm, with a generator generating feasible sequences and an evaluator selecting the best sequence based on the estimated list utility. However, these methods still face two issues. Firstly, due to the goal inconsistency problem between the evaluator and generator, the generator tends to fit the local optimal solution of exposure distribution rather than combinatorial space optimization. Secondly, the strategy of generating target items one by one is difficult to achieve optimality because it ignores the information of subsequent items. To address these issues, we propose a utilizing Neighbor Lists model for Generative Reranking (NLGR), which aims to improve the performance of the generator in the combinatorial space. NLGR follows the evaluator-generator paradigm and improves the generator's training and generating methods. Specifically, we use neighbor lists in combination space to enhance the training process, making the generator perceive the relative scores and find the optimization direction. Furthermore, we propose a novel sampling-based non-autoregressive generation method, which allows the generator to jump flexibly from the current list to any neighbor list. Extensive experiments on public and industrial datasets validate NLGR's effectiveness and we have successfully deployed NLGR on the Meituan food delivery platform.