Judicial efficiency is critical to social stability. However, in many countries worldwide, grassroots courts face substantial case backlogs, and judicial decisions remain heavily dependent on judges' cognitive efforts, with insufficient intelligent tools to enhance efficiency. To address this issue, we propose a highly efficient law article recommendation approach combining a Knowledge Graph (KG) and a Large Language Model (LLM). First, we construct a Case-Enhanced Law Article Knowledge Graph (CLAKG) to store current law articles, historical case information, and their interconnections, alongside an LLM-based automated construction method. Building on this, we propose a closed-loop law article recommendation framework integrating graph embedding-based retrieval and KG-grounded LLM reasoning. Experiments on judgment documents from China Judgments Online demonstrate that our method boosts law article recommendation accuracy from 0.549 to 0.694, outperforming strong baselines significantly. To support reproducibility and future research, all source code and processed datasets are publicly available on GitHub (see Data Availability Statement).