Natural language generation (NLG) metrics play a central role in evaluating generated texts, but are not well suited for the structural and legal characteristics of patent documents. Large language models (LLMs) offer strong potential in automating patent generation, yet research on evaluating LLM-generated patents remains limited, especially in evaluating the generation quality of patent claims, which are central to defining the scope of protection. Effective claim evaluation requires addressing legal validity, technical accuracy, and structural compliance. To address this gap, we introduce PatentScore, a multi-dimensional evaluation framework for assessing LLM-generated patent claims. PatentScore incorporates: (1) hierarchical decomposition for claim analysis; (2) domain-specific validation patterns based on legal and technical standards; and (3) scoring across structural, semantic, and legal dimensions. Unlike general-purpose NLG metrics, PatentScore reflects patent-specific constraints and document structures, enabling evaluation beyond surface similarity. We evaluate 400 GPT-4o-mini generated Claim 1s and report a Pearson correlation of $r = 0.819$ with expert annotations, outperforming existing NLG metrics. Furthermore, we conduct additional evaluations using open models such as Claude-3.5-Haiku and Gemini-1.5-flash, all of which show strong correlations with expert judgments, confirming the robustness and generalizability of our framework.