In order to buy life insurance on another person the insurance company requires an insurable interest between the people.
Insurable interest basically means you stand to lose financially if the person you want to insure were to die.
Insurable interest does exist between parents and their children, spouses, siblings, relatives, and business partners, etc.
However, in order for a parent to buy a life insurance policy on their child, you would need your child's consent and permission, signature on the application, and the child may need to answer some health questions, and/or take a physical exam.
However, there are life insurance companies that allow a parent to buy a life insurance policy on his child. here's how you can learn more and request life insurance quotes for adult children.