If I am a minor, can I do my tax refund under a parents bank account?

[fanfare]

your parents probably don't want your name added to their bank account.

Take a check. You can endorse it over to your parents so they can cash it for you.

[Anita01]

If you mean can you have a refund deposited to a parent's bank account, probably not.  Banks are extremely picky about taking deposits or paying bills out of accounts where the name of the person involved is not on the account.  You should ask your parents about having your name added to the account and have them ask the bank how long before that would be effective so you know when to file your return.