Recently, large language models (LLMs) have demonstrated remarkable potential as an intelligent agent. However, existing researches mainly focus on enhancing the agent's reasoning or decision-making abilities through well-designed prompt engineering or task-specific fine-tuning, ignoring the procedure of exploration and exploitation. When addressing complex tasks within open-world interactive environments, these methods exhibit limitations. Firstly, the lack of global information of environments leads to greedy decisions, resulting in sub-optimal solutions. On the other hand, irrelevant information acquired from the environment not only adversely introduces noise, but also incurs additional cost. This paper proposes a novel approach, Weak Exploration to Strong Exploitation (WESE), to enhance LLM agents in solving open-world interactive tasks. Concretely, WESE involves decoupling the exploration and exploitation process, employing a cost-effective weak agent to perform exploration tasks for global knowledge. A knowledge graph-based strategy is then introduced to store the acquired knowledge and extract task-relevant knowledge, enhancing the stronger agent in success rate and efficiency for the exploitation task. Our approach is flexible enough to incorporate diverse tasks, and obtains significant improvements in both success rates and efficiency across four interactive benchmarks.