PCBRouteAgent is a multimodal PCB routing agent that mimics how human engineers coordinate global strategy with local execution. The Global Routing Planner consumes board images together with structured electrical and geometric data, and produces a connection topology, routing order, corridor definitions, and layer‑transition points. The Detailed Routing Executor then drives KiCad’s native routing engine to realize these guides, applying bounded local recovery when conflicts arise. Unresolved failures are returned as structured feedback, allowing the planner to revise its guidance while preserving already accepted routes. Evaluation on 247 synthetic and real boards across four PCBWorld‑Bench splits (D2, D3‑A, D3‑B, D3‑C) yields clean‑pass rates of 100%, 94.9%, 100% and 40% respectively. On the three real‑world subsets, PCBRouteAgent outperforms the best baseline by 13.9, 36 and 10 percentage points in clean‑pass rate.\n\nReview: This study demonstrates a viable integration of LLMs with traditional EDA tools, especially highlighting the benefit of a global‑local coordination loop and structured feedback. It marks a significant step toward fully automated PCB design and suggests promising directions for future research.