Harry Potter's grandparents all died before the series began and very little is known about them. His maternal grandparents were both muggles, his father's parents were both pure-blood wizards.
His father's parents came from a long line of pure-blood wizards and were very wealthy. They had their son James late in life and he was their only child.
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It never mentions Harry's parents in the entire series, all except for the chapter in the first book, called the Mirror of Erised. They never mention the names, though, just their presence.