My first reaction to this was probably a whale and the biggest whale I could think of which is also the biggest animal we know of is the Blue Whale. However after a bit of searching and reading I've found that this is not the case. The animal with the largest brain in existence is however still a whale.
A: The Sperm Whale with a brain of 7kg
Compared to a 5kg brain from the largest animal the Blue Whale.
Source - http://news.softpedia.com/news/13-Amazing-Facts-Ab...
Also a bit more searching on sperm whale brains finds a different heavier weight for the sperm whale brain of 7.82 kg and that elephants (the largest land animal) come in second at 16.5 pounds which is around 7.48kg