 Modern natural language generation paradigms require a good decoding strategy to obtain quality sequences out of the model. Beam search yields high-quality but low diversity outputs; stochastic approaches suffer from high variance and sometimes low quality, but the outputs tend to be more natural and creative. In this work, we propose a deterministic search algorithm balancing both quality and diversity. We first investigate the vanilla best-first search (BFS) algorithm and then propose the Best-k *Search* algorithm.  Inspired by BFS, we greedily expand the top k nodes, instead of only the first node, to boost efficiency and diversity. Upweighting recently discovered nodes accompanied by heap pruning ensures the completeness of the search procedure. Experiments on four NLG tasks, including question generation, commonsense generation, text summarization, and translation, show that best-k search yields more diverse and natural outputs compared to strong baselines, while our approach maintains high text quality. The proposed algorithm is parameter-free, lightweight, efficient, and easy to use1. 