Artificial Intelligence (AI) has received an increasing amount of attention in multiple areas. The uncertainties and risks in AI-powered systems have created reluctance in their wild adoption. As an economic solution to compensate for potential damages, AI liability insurance is a promising market to enhance the integration of AI into daily life. In this work, we use an AI-powered E-diagnosis system as an example to study AI liability insurance. We provide a quantitative risk assessment model with evidence-based numerical analysis. We discuss the insurability criteria for AI technologies and suggest necessary adjustments to accommodate the features of AI products. We show that AI liability insurance can act as a regulatory mechanism to incentivize compliant behaviors and serve as a certificate of high-quality AI systems. Furthermore, we suggest premium adjustment to reflect the dynamic evolution of the inherent uncertainty in AI. Moral hazard problems are discussed and suggestions for AI liability insurance are provided.