Large Language Models (LLMs) are increasingly employed in zero-shot documents ranking, yielding commendable results. However, several significant challenges still persist in LLMs for ranking: (1) LLMs are constrained by limited input length, precluding them from processing a large number of documents simultaneously; (2) The output document sequence is influenced by the input order of documents, resulting in inconsistent ranking outcomes; (3) Achieving a balance between cost and ranking performance is quite challenging. To tackle these issues, we introduce a novel documents ranking method called TourRank, which is inspired by the tournament mechanism. This approach alleviates the impact of LLM's limited input length through intelligent grouping, while the tournament-like points system ensures robust ranking, mitigating the influence of the document input sequence. We test TourRank with different LLMs on the TREC DL datasets and the BEIR benchmark. Experimental results show that TourRank achieves state-of-the-art performance at a reasonable cost.