As far as is known, Colomb's Game was the first naval war game. Invented by Captain Colomb of the British Navy in 1878, it appeared 54 years after Lieutenant von Reisswitz's "War Game of Prussia," the first of the land warfare games.
McHugh, Francis J.
"Eighty Years of War Gaming,"
Naval War College Review: Vol. 22
, Article 8.
Available at: http://digital-commons.usnwc.edu/nwc-review/vol22/iss3/8