Large Language Models (LLMs) have achieved significant success in various natural language processing tasks, but how wireless communications can support LLMs has not been extensively studied. In this paper, we propose a wireless distributed LLMs paradigm based on Mixture of Experts (MoE), named WDMoE, deploying LLMs collaboratively across edge servers of base station (BS) and mobile devices in the wireless communications system. Specifically, we decompose the MoE layer in LLMs by deploying the gating network and the preceding neural network layer at BS, while distributing the expert networks across the devices. This arrangement leverages the parallel capabilities of expert networks on distributed devices. Moreover, to overcome the instability of wireless communications, we design an expert selection policy by taking into account both the performance of the model and the end-to-end latency, which includes both transmission delay and inference delay. Evaluations conducted across various LLMs and multiple datasets demonstrate that WDMoE not only outperforms existing models, such as Llama 2 with 70 billion parameters, but also significantly reduces end-to-end latency.