Government operates Government Compensation System to make compensation for victim from car accident by hit-and-run or uninsured driver under the article 30 (1) 1. & 2. in the Act on Guarantee of Compensation for Loss Caused by Automobile. And the insurers of Government Compensation System commissioned by Ministry of Land, Infrastructure and Transport performed subrogation right to inflictor who has liability for damages apropos of victims. Whereupon, there are some arguments as regards subrogation right that is to protect double benefit of victims by the insurers of Government Compensation System commissioned by Ministry of Land, Infrastructure and Transport, i.e., the insurers exercising rights to demand a reimbursement against for inflictor who has liability for damages apropos of victims in the Act on Guarantee of Compensation for Loss Caused by Automobile and other insurers which compensated victims from car accident by hit-and-run or uninsured driver priority to the insurers of Government Compensation System could be acting right to indemnity to the insurers. Therefor this article is intended to suggest that insurers of Government Compensation System need to exercise the right to indemnity for parents of minor and family living in the same house who take an charge for liability for damage at the Act on Guarantee of Compensation for Loss Caused by Automobile. And also expressed that right to indemnity of National Health Insurance Corporation and designated driver insurer compensated victim who got a accident from hit-and-run or uninsured driver in stead of insurers of Government Compensation System was restricted to insurers of Government Compensation System.