Semantic communication (SC) is an emerging intelligent paradigm, offering solutions for various future applications like metaverse, mixed-reality, and the Internet of everything. However, in current SC systems, the construction of the knowledge base (KB) faces several issues, including limited knowledge representation, frequent knowledge updates, and insecure knowledge sharing. Fortunately, the development of the large AI model provides new solutions to overcome above issues. Here, we propose a large AI model-based SC framework (LAM-SC) specifically designed for image data, where we first design the segment anything model (SAM)-based KB (SKB) that can split the original image into different semantic segments by universal semantic knowledge. Then, we present an attention-based semantic integration (ASI) to weigh the semantic segments generated by SKB without human participation and integrate them as the semantic-aware image. Additionally, we propose an adaptive semantic compression (ASC) encoding to remove redundant information in semantic features, thereby reducing communication overhead. Finally, through simulations, we demonstrate the effectiveness of the LAM-SC framework and the significance of the large AI model-based KB development in future SC paradigms.