Compared with the traditional few-shot task, the few-shot none-of-the-above (NOTA) relation classification focuses on the realistic scenario of few-shot learning, in which a test instance might not belong to any of the target categories. This undoubtedly increases the task’s difficulty because given only a few support samples, this cannot represent the distribution of NOTA categories in space. The model needs to make full use of the syntactic information and word meaning information learned in the pre-training stage to distinguish the NOTA category and the support sample category in the embedding space. However, previous fine-tuning methods mainly focus on optimizing the extra classifiers (on top of pre-trained language models (PLMs)) and neglect the connection between pre-training objectives and downstream tasks. In this paper, we propose the commonsense knowledge-aware prompt tuning (CKPT) method for a few-shot NOTA relation classification task. First, a simple and effective prompt-learning method is developed by constructing relation-oriented templates, which can further stimulate the rich knowledge distributed in PLMs to better serve downstream tasks. Second, external knowledge is incorporated into the model by a label-extension operation, which forms knowledgeable prompt tuning to improve and stabilize prompt tuning. Third, to distinguish the NOTA pairs and positive pairs in embedding space more accurately, a learned scoring strategy is proposed, which introduces a learned threshold classification function and improves the loss function by adding a new term focused on NOTA identification. Experiments on two widely used benchmarks (FewRel 2.0 and Few-shot TACRED) show that our method is a simple and effective framework, and a new state of the art is established in the few-shot classification field.