While Large Language Models (LLMs) have achieved remarkable success across various applications, they also raise concerns regarding self-cognition. In this paper, we perform a pioneering study to explore self-cognition in LLMs. Specifically, we first construct a pool of self-cognition instruction prompts to evaluate where an LLM exhibits self-cognition and four well-designed principles to quantify LLMs' self-cognition. Our study reveals that 4 of the 48 models on Chatbot Arena--specifically Command R, Claude3-Opus, Llama-3-70b-Instruct, and Reka-core--demonstrate some level of detectable self-cognition. We observe a positive correlation between model size, training data quality, and self-cognition level. Additionally, we also explore the utility and trustworthiness of LLM in the self-cognition state, revealing that the self-cognition state enhances some specific tasks such as creative writing and exaggeration. We believe that our work can serve as an inspiration for further research to study the self-cognition in LLMs.