Your father's death certificate should give the names of his parents, assuming the informant knew their identity.If you know his date of death and the county where he died, you can get a copy of his death certificate from the county clerk.
Your father's birth certificate would certainly give the names of his parents, unless the mother was unwed and did not name the father.If you know when your father was born and in what county, you can get a copy of his birth certificate from the county clerk.
You can also get a copy of his Social Security application, which should include the names of his parents.If you can find him in the SSDI (Social Security Death Index), you can order a copy of the application:
When you find him, note there is a link over to the right that says "SS-5 Letter."It's the text of a letter you can use to request his application.Just copy the text into your word processor and be certain to add that he is your father.If you're not next-of-kin, they will redact the names of the parents.
Gathering the birth, marriage, and death certificates of your parents and grandparents is a rather standard step in *documenting* your genealogy, even if you already know all the names, dates, and places.Their crucial if you don't.