Recently, Large Language Models (LLMs) have been used for knowledge-based Visual Question Answering (VQA). Despite the encouraging results of previous studies, prior methods prompt LLMs to predict answers directly, neglecting intermediate thought processes. We argue that prior methods do not sufficiently activate the capacities of LLMs. We propose a framework called PLRH that Prompts LLMs with Rationale Heuristics for knowledge-based VQA. The PLRH prompts LLMs with Chain of Thought (CoT) to generate rationale heuristics, i.e., intermediate thought processes, and then leverages the rationale heuristics to inspire LLMs to predict answers. Experiments show that our approach outperforms the existing baselines by more than 2.2 and 2.1 on OK-VQA and A-OKVQA, respectively.