An important corporate executive plays a very important role in the establishment and performance of decisions. After the Tort liability aggravates, the corporate executive has compensatory responsibility to the third party. If acting against the operating obligation in the economic activity, the tort liability is hard burdened by the corporate executives. Therefore, companies use the liability insurance to reduce operating risk for their executives. And the Directors and Officers Liability Insurance (D&O liability insurance) is very popular abroad. In recent years the D&O liability insurance is more and more valued by Taiwan companies. Internationally, the corruption of corporate emerges continuously. And the reason is that the company important operators violate the business ethics. In addition the company important operators are negligent to their operating duty of the third party and shareholders. The corporate corruption causes the economic disorder. So our government establishes and revises ordinances in order to prevent the tort from happening. Relatively, company important operator's legal liability also becomes more aggravated. This study focuses on the research of present legal rules, and discusses about the corporate executives' legal status and the responsibility of duty by analyzing collections, reading the theory and researching legal judicial precedent. Then, to understand the relationship of the fault of tort and D&O liability insurance is helping us to know the function and the effect of D&O liability insurance.