Listwise ranking based on Large Language Models (LLMs) has achieved state-of-the-art performance in Information Retrieval (IR). However, their effectiveness often depends on LLMs with massive parameter scale (e.g., GPT-4) and computationally expensive sliding window processing, leading to substantial efficiency bottlenecks. In this paper, we propose a Collaborative Ranking framework (CoRanking) for LLM-based listwise ranking. Specifically, we strategically combine an efficient small reranker and an effective large reranker, and jointly optimize with a novel reinforcement learning method (RL). The small reranker performs initial passage ranking, effectively filtering the candidate set to a condensed top-k list (e.g., top-20 passages), and the large reranker (with stronger ranking capability) then reranks only this condensed subset rather than the full list, significantly improving efficiency. We further address that directly passing the top-ranked passages from the small reranker to the large reranker is suboptimal because of the LLM's strong positional bias in processing input sequences. To resolve this issue, we propose a passage order adjuster learned by RL that dynamically reorders the top passages returned by the small reranker to better align with the large LLM's input preferences. Our extensive experiments across three IR benchmarks demonstrate that CoRanking achieves superior efficiency, reducing ranking latency by approximately 70% while simultaneously improving effectiveness, compared to standalone large listwise reranker.