A life insurance policy is a contract and you need to be an adult to sign a legally binding contract.
However, I believe the parent or legal guardian may buy a life insurance policy on behalf of the minor.
So, the grand parent may buy a life insurance on their grand child, if the grandparent's child is too young to own the life insurance policy.
However, you should review this question with the life insurance company, and/or your life insurance agent to understand the proper set up of the life insurance policy and who can legally buy the life insurance.
Here's how you can learn more about life insurance for children and how it works.