This paper proposes VerilogLAVD, a novel method for early detection of hardware vulnerabilities. To overcome the limitations of existing methods requiring expert knowledge, this paper presents an approach that utilizes a large-scale language model (LLM) to detect vulnerabilities in Verilog code. The Verilog Property Graph (VeriPG), which represents Verilog code in an integrated manner, combines syntactic and semantic information. Using the LLM, VeriPG-based detection rules are generated from Common Weakness Enumeration (CWE) descriptions. These rules are then used by a rule executor that searches VeriPG for potential vulnerabilities. Experimental results on 77 Verilog designs demonstrate an F1-score of 0.54 for 12 CWE types, demonstrating F1-score improvements of 0.31 and 0.27, respectively, compared to the LLM alone or an external knowledge base.