In recent years, the rise of large language models (LLMs) has made it possible to directly achieve named entity recognition (NER) without any demonstration samples or only using a few samples through in-context learning (ICL). However, standard ICL only helps LLMs understand task instructions, format and input-label mapping, but neglects the particularity of the NER task itself. In this paper, we propose a new prompting framework P-ICL to better achieve NER with LLMs, in which some point entities are leveraged as the auxiliary information to recognize each entity type. With such significant information, the LLM can achieve entity classification more precisely. To obtain optimal point entities for prompting LLMs, we also proposed a point entity selection method based on K-Means clustering. Our extensive experiments on some representative NER benchmarks verify the effectiveness of our proposed strategies in P-ICL and point entity selection.