Donald Trump has made a lot of promises this year, and an old signed copy of his book shows he's true to his word ... certainly when it involves his hair.

Gary Zimet is selling an autographed "The Way to the Top: The Best Business Advice I Ever Received" book for $18,000 on his site, MomentsInTime.com. He tells us the book came from a man who attended a Trump speaking engagement in 2005 and asked the Donald to sign it for his wife Carol ... who loved his hair.