Technically the Necronomicon exist, in many forms actually. Do any of them predate the essay "History of the Necronomicon," by H.P. Lovecraft? No, I'm afraid. No, I'm sorry, but any site reporting the validity of the Necronomicon as seen in the Evil Dead films is full of it. Sam Raimi admits that he got the idea in a college literature class whilst studying H.P. Lovecraft. The fictional Necronomicon most well reckognized is indeed Simon's but there have been many versions that even predate that one. For an interesting history of the various hoax Necronomicons check out the book "The Necronomicon Files," I borrowed it from the bookstore that I work at and it's quite the interesting read.
The actual Necronomicon is not called the Necronomicon, the clue to it's content is the in the name...Necronomicon: literally " The List Of Dead Names".
The book that influenced HPL was a grimoire that was set out in it's established form in the early 14th century and is actually still in print today.