This issue is a variant of Godzilla: Kingdom of Monsters (IDW, 2011 series) #1 [Cover A]. There exist further variants.
Creative Consultant: Chris Mowry
There are four regular variant covers for this issue. Additional variant covers were made for comic book stores who purchased at least 500 copies of Godzilla #1. They show Godzilla smashing their store. The first issue shows the covers for 75 participating comic book stores. IDW arranged a second print of variant covers which included 23 more variant covers.
Stores were drawn by Matt Frank (about 30 of them solo), Cassandra Gibbs, Joana Lafuente, Gordon Purcell, Alan Robinson, Kris Carvajel and Jamie Snell. The covers were colored by Matt Frank, Liam Shalloo, John Paul Bove, Kote Carvajel and Josh Perez. [information from http://www.scifijapan.com/articles/2011/02/25/covering-godzilla/. Article appears to have been written before second printing covers were done, but presumably they were a similar team effort.]