In the hearing, attorneys for British authors Michael Baigent and Richard Leigh said a lower court's adverse ruling was "based on a misunderstanding of the law and of the claim," The Times of London said.
The men claimed Brown stole the central theme from their book, "The Holy Blood and the Holy Grail," for his thriller. A lower court ruling cleared Brown of the charge.
Jonathan Rayner James told the three-judge panel his clients' original claim -- "that the theme appropriated by Brown and used in 'The Da Vinci Code' was a substantial part of (their) copyright" -- was still valid.
In clearing Brown, the lower court ruled Baigent and Leigh should pay 85 percent of Random House court costs, which were estimated at nearly $2.5 million, as well as their own legal fees. Random House was the publisher of both books.
"The Da Vinci Code" explores the theory that Jesus and Mary Magdalene were married and had a child, and that the bloodline continued through the centuries.
Celebrity Families of 2014 [PHOTOS]