With fast development and penetration of Electric Vehicles (EVs), the charging demand of EVs has grow over tenfold in recent years in major citys. In this work, we aim at the issues raised by the EV clusters charging demand, and proposed a LLM-MBPO Cooperation framework for smart operations of EV clusters with active distribution grids. First, a large language model (LLM) with model-based policy Optimization (MBPO) framework is developed. The comprehensive interactive capability of LLM is used to bridge the gap between the uncertain charging operations and the model settings of MBPO. Second, the LLM is fine tuned power distribution system operation and optimization knowledge, to fit it the role of regulating the MBPO. The MBPO is continuous action space deep reinforcement learning algorithm, which is managing the charging operations of EV clusters. Lastly, the proposed framework is tested with case studies and verified that it can effectively save the charging cost of EV clusters while providing operation supports to the distribution grid.