Large language models (LLMs) are increasingly used in everyday life and research. One of the most common use cases is conversational interactions, enabled by the language generation capabilities of LLMs. Just as between two humans, a conversation between an LLM-powered entity and a human depends on the personality of the conversants. However, measuring the personality of a given LLM is currently a challenge. This article introduces the Language Model Linguistic Personality Assessment (LMLPA), a system designed to evaluate the linguistic personalities of LLMs. Our system helps to understand LLMs’ language generation capabilities by quantitatively assessing the distinct personality traits reflected in their linguistic outputs. Unlike traditional human-centric psychometrics, the LMLPA adapts a personality assessment questionnaire, specifically the Big Five Inventory, to align with the operational capabilities of LLMs, and also incorporates the findings from previous language-based personality measurement literature. To mitigate sensitivity to the order of options, our questionnaire is designed to be open-ended, resulting in textual answers. Thus, the Artificial Intelligence (AI) rater is needed to transform ambiguous personality information from text responses into clear numerical indicators of personality traits. Utilizing Principal Component Analysis and reliability validation methods, our findings demonstrate that LLMs possess distinct personality traits that can be effectively quantified by the LMLPA. This research contributes to Human-Centered AI and Computational Linguistics, providing a robust framework for future studies to refine AI personality assessments and expand their applications in multiple areas, including education and manufacturing.