Recommendation systems are widely used in e-commerce websites and online platforms to address information overload. However, existing systems primarily rely on historical data and user feedback, making it difficult to capture user intent transitions. Recently, Knowledge Base (KB)-based models are proposed to incorporate expert knowledge, but it struggle to adapt to new items and the evolving e-commerce environment. To address these challenges, we propose a novel Large Language Model based Complementary Knowledge Enhanced Recommendation System (LLM-KERec). It introduces an entity extractor that extracts unified concept terms from item and user information. To provide cost-effective and reliable prior knowledge, entity pairs are generated based on entity popularity and specific strategies. The large language model determines complementary relationships in each entity pair, constructing a complementary knowledge graph. Furthermore, a new complementary recall module and an Entity-Entity-Item (E-E-I) weight decision model refine the scoring of the ranking model using real complementary exposure-click samples. Extensive experiments conducted on three industry datasets demonstrate the significant performance improvement of our model compared to existing approaches. Additionally, detailed analysis shows that LLM-KERec enhances users' enthusiasm for consumption by recommending complementary items. In summary, LLM-KERec addresses the limitations of traditional recommendation systems by incorporating complementary knowledge and utilizing a large language model to capture user intent transitions, adapt to new items, and enhance recommendation efficiency in the evolving e-commerce landscape.