Large Language Models (LLMs) are widely used in many different domains, but because of their limited interpretability, there are questions about how trustworthy they are in various perspectives, e.g., truthfulness and toxicity. Recent research has started developing testing methods for LLMs, aiming to uncover untrustworthy issues, i.e., defects, before deployment. However, systematic and formalized testing criteria are lacking, which hinders a comprehensive assessment of the extent and adequacy of testing exploration. To mitigate this threat, we propose a set of multi-level testing criteria, LeCov, for LLMs. The criteria consider three crucial LLM internal components, i.e., the attention mechanism, feed-forward neurons, and uncertainty, and contain nine types of testing criteria in total. We apply the criteria in two scenarios: test prioritization and coverage-guided testing. The experiment evaluation, on three models and four datasets, demonstrates the usefulness and effectiveness of LeCov.