Finite State Machines (FSMs) play a critical role in implementing control logic for Systems-on-Chip (SoC). Traditionally, FSMs are implemented by hardware engineers through Verilog coding, which is often tedious and time-consuming. Recently, with the remarkable progress of Large Language Models (LLMs) in code generation, LLMs have been increasingly explored for automating Verilog code generation. However, LLM-generated Verilog code often suffers from security vulnerabilities, which is particularly concerning for security-sensitive FSM implementations. To address this issue, we propose SecFSM, a novel method that leverages a security-oriented knowledge graph to guide LLMs in generating more secure Verilog code. Specifically, we first construct a FSM Security Knowledge Graph (FSKG) as an external aid to LLMs. Subsequently, we analyze users' requirements to identify vulnerabilities and get a list of vulnerabilities in the requirements. Then, we retrieve knowledge from FSKG based on the vulnerabilities list. Finally, we construct security prompts based on the security knowledge for Verilog code generation. To evaluate SecFSM, we build a dedicated dataset collected from academic datasets, artificial datasets, papers, and industrial cases. Extensive experiments demonstrate that SecFSM outperforms state-of-the-art baselines. In particular, on a benchmark of 25 security test cases evaluated by DeepSeek-R1, SecFSM achieves an outstanding pass rate of 21/25.