Court efficiency is vital for social stability. However, in most countries around the world, the grassroots courts face case backlogs, with decisions relying heavily on judicial personnel's cognitive labor, lacking intelligent tools to improve efficiency. To address this issue, we propose an efficient law article recommendation approach utilizing a Knowledge Graph (KG) and a Large Language Model (LLM). Firstly, we propose a Case-Enhanced Law Article Knowledge Graph (CLAKG) as a database to store current law statutes, historical case information, and correspondence between law articles and historical cases. Additionally, we introduce an automated CLAKG construction method based on LLM. On this basis, we propose a closed-loop law article recommendation method. Finally, through a series of experiments using judgment documents from the website "China Judgements Online", we have improved the accuracy of law article recommendation in cases from 0.549 to 0.694, demonstrating that our proposed method significantly outperforms baseline approaches.