Curiosity serves as a fundamental construct in human cognition.Inspired by curiosity, reinforcement learning with intrinsic rewards for large language models (LLMs) has shown substantial potential.However, it remains unclear whether existing curiosity-driven methods genuinely reflect curiosity-like behaviors in LLMs, and to what extent psychological notions of curiosity can be transferred to these models. In this work, we propose a psychology-inspired framework to evaluate and leverage curiosity in LLMs.We adapt the Five-Dimensional Curiosity scale Revised (5DCR) to LLMs and combine questionnaire-based self reports with behavioral study.We find that although LLMs can exhibit curiosity-like behavioral patterns resembling those of humans, such patterns do not reflect an intrinsic trait of curiosity.Building on this insight, we design a curiosity-driven thinking pipeline to examine the functional role of human-like curious behaviors. Experiments show that instructing LLMs to emulate curious strategies leads to better performance on selected downstream tasks, indicating that mimicking curious behaviors holds promise for reasoning enhancement.