Commonsense Question Answering (CQA) aims to answer questions that require human commonsense. Closed-book CQA, as one of the subtasks, requires the model to answer questions without retrieving external knowledge, which emphasizes the importance of the model's problem-solving ability. Most previous methods relied on large-scale pre-trained models to generate question-related knowledge while ignoring the crucial role of skills in the process of answering commonsense questions. Generally, skills refer to the learned ability in performing a specific task or activity, which are derived from knowledge and experience. In this paper, we introduce a new approach named Dynamic Skill-aware Commonsense Question Answering (DSCQA), which transcends the limitations of traditional methods by informing the model about the need for each skill in questions and utilizes skills as a critical driver in CQA process. To be specific, DSCQA first employs commonsense skill extraction module to generate various skill representations. Then, DSCQA utilizes dynamic skill module to generate dynamic skill representations. Finally, in perception and emphasis module, various skills and dynamic skill representations are used to help question-answering process. Experimental results on two publicly available CQA datasets show the effectiveness of our proposed model and the considerable impact of introducing skills.