Large Language Models (LLMs) have achieved remarkable success across a wide range of applications. However, individual LLMs often produce inconsistent, biased, or hallucinated outputs due to limitations in their training corpora and model architectures. Recently, collaborative frameworks such as the Multi-LLM Network (MultiLLMN) have been introduced, enabling multiple LLMs to interact and jointly respond to user queries. Nevertheless, MultiLLMN architectures raise critical concerns regarding the reliability and security of the generated content, particularly in open environments where malicious or compromised LLMs may be present. Moreover, reliance on centralized coordination undermines system efficiency and introduces single points of failure. In this paper, we propose a novel Trusted MultiLLMN framework, driven by a Weighted Byzantine Fault Tolerance (WBFT) blockchain consensus mechanism, to ensure the reliability, security, and efficiency of multi-LLM collaboration. In WBFT, voting weights are adaptively assigned to each LLM based on its response quality and trustworthiness, incentivizing reliable behavior, and reducing the impact of malicious nodes. Extensive simulations demonstrate that WBFT significantly improves both consensus security and efficiency compared to classical and modern consensus mechanisms, particularly under wireless network conditions. Furthermore, our evaluations reveal that Trusted MultiLLMN supported by WBFT can deliver higher-quality and more credible responses than both single LLMs and conventional MultiLLMNs, thereby providing a promising path toward building robust, decentralized AI collaboration networks.