Autonomous navigation systems, as essential components of autonomous ships, with their performance in terms of validity and reliability serving as crucial criteria for verification. This study proposes an efficient testing method based on high-coverage scenario generation to evaluate autonomous navigation systems in a simulation-based environment. At first, a test scenario model is developed by abstracting and discretizing the real-world parameter space. Then an environmental risk distribution index is introduced to mitigate the frequency of extremely dangerous scenarios. To address the inefficiency of simulation-based testing, a grey-box based simulation acceleration method is proposed to optimize the testing process. Simulation experiments demonstrate that the coverage of the generated test scenario set is optimized with a higher confidence level, while the proposed acceleration method significantly improves testing efficiency. The results indicate that this method achieves efficient and comprehensive testing of autonomous navigation systems, contributing to the advancement of autonomous ship technology.