Applying Large Language Models (LLM) to solve math problems is one of the hottest research topics at present. Traditional Chain-of-Thought-based methods typically generate the reasoning path in a chain structure, leading to unnecessary interference caused by non-zero self-attention among weakly related reasoning steps. Such a setting also differs from humans’ typical graph-structured reasoning habit (with an inter-step relationship graph in mind). To solve the problem, this paper proposes a novel decoding method for Transformer-based LLM, named Self-attention-based Graph-of-Thought (SaGoT). SaGoT constructs a thought graph simultaneously as an LLM inference (based on a newly defined inter-step self-attention indicator), and generates reasoning steps with a novel graph-structured self-attention mechanism. It is a significant contribution for SaGoT to enable an LLM’s graph-like reasoning ability by modifying its inner working operations, compared to SOTA prompting methods that are ex-post, rely on huge LLMs and redundant reasoning step generation to form a graph (inefficient & non-human-like). In addition, SaGoT is a training-free technique that can be seamlessly incorporated into pre-trained Transformer-based LLMs. Our experimental results have shown that SaGoT could significantly enhance mathematical reasoning accuracy without the reliance on huge computationally over-expensive LLMs. It also avoids SOTA methods’ performance degradation issues when the LLM is too small to comprehend complex prompts. Moreover, SaGoT integrates intrinsic interpretability into the LLM’s reasoning procedure, intuitively assisting humans in understanding how an LLM views the relationships among its reasoning steps, and why the LLM succeeds or fails.