Chain-of-thought (CoT) reasoning boosts large language models' (LLMs) performance on complex tasks but faces two key limitations: a lack of reliability when solely relying on LLM-generated reasoning chains and lower reasoning performance from natural language prompts compared with code prompts. To address these issues, we propose CoT-RAG, a novel reasoning framework with three key designs: (i) Knowledge Graph-driven CoT Generation, featuring knowledge graphs to modulate reasoning chain generation of LLMs, thereby enhancing reasoning credibility; (ii) Learnable Knowledge Case-aware RAG, which incorporates retrieval-augmented generation (RAG) into knowledge graphs to retrieve relevant sub-cases and sub-descriptions, providing LLMs with learnable information; (iii) Pseudo Program Prompting Execution, which promotes greater logical rigor by guiding LLMs to execute reasoning tasks as pseudo-programs. Evaluations on nine public datasets spanning three reasoning tasks reveal significant accuracy gains-ranging from 4.0% to 44.3%-over state-of-the-art methods. Furthermore, tests on four domain-specific datasets demonstrate exceptional accuracy and efficient execution, underscoring its practical applicability and scalability. Our code and data are available at https: //github.com/hustlfy123/CoT-RAG.