Recent advances in decision-making policies have led to significant progress in fields such as autonomous driving and robotics. However, testing these policies remains crucial with the existence of critical scenarios that may threaten their reliability. Despite ongoing research, challenges such as low testing efficiency and limited diversity persist due to the complexity of the decision-making policies and their environments. To address these challenges, this paper proposes an adaptable Large Language Model (LLM)-driven online testing framework to explore critical and diverse testing scenarios for decision-making policies. Specifically, we design a "generate-test-feedback" pipeline with templated prompt engineering to harness the world knowledge and reasoning abilities of LLMs. Additionally, a multi-scale scenario generation strategy is proposed to address the limitations of LLMs in making fine-grained adjustments, further enhancing testing efficiency. Finally, the proposed LLM-driven method is evaluated on five widely recognized benchmarks, and the experimental results demonstrate that our method significantly outperforms baseline methods in uncovering both critical and diverse scenarios. These findings suggest that LLM-driven methods hold significant promise for advancing the testing of decision-making policies.