Chain-of-Thought prompting has improved reasoning capability of large language models (LLM). However, it still is challenging to guarantee the effectiveness and stability for questions requiring complicated reasoning. Recently, Plan-and-Solve prompting enhances the reasoning capability for complex questions by planning the solution steps firstly and then solving them step by step, but it suffers the difficulty to represent and execute the problem-solving logic of complex questions. To deal with these challenges, in this work, we propose a novel Plan-and-Solve prompting method based on Question Decomposition Meaning Representation (QDMR). Specifically, this method first allows the LLM to generate a QDMR graph to represent the problem-solving logic, which is a directed acyclic graph composed of sub-questions. Then, the LLM generates a specific solving process based on the QDMR graph. When solving each sub-question, it can locate the preceding sub-questions and their answers according to the QDMR graph, and then utilize this information for solution. Compared with existing Plan-and-Solve prompting techniques, our method can not only represent the problem-solving logic of complicated questions more accurately with the aid of QDMR graph, but also deliver the dependence information accurately for different solution steps according to the QDMR graph. In addition, with the supervised fine-tuning on the Allen Institute dataset, the decomposing capability of LLM for complicated questions can be considerably enhanced. Extensive experiments show that our method has achieve a great significance in arithmetic reasoning and commonsense reasoning task by comparing the classical Chain-of-Thought prompting and Plan-and-Solve prompting techniques, and the improvements achieved are even greater for problems with more reasoning steps.