After doing some extensive research I have located the confirmed largest alligator gar ever caught and confirmed, but the thing is there are different alligator gar records depending on how the person when about catching the fish, so I list all of them.
First there is the record for catching a alligator gar fish with rod & reel which was actually set way back in 1951 and has yet to be beat, this alligator gar weighed 279 lbs. There were no pictures of this catch for years, until a relative found a photo and eventually made it public many years later(the picture below).
The current record alligator gar caught with a net was set recently in 2011 by Kenny Williams in Mississippi. He snagged this large 327 lb specimen.
If you are familiar with alligator gar fishing then you would know it's very hard to catch this gar with the usual rod & reel tactic, this is because of their bony jaws. So it comes to no surprise that the world record alligator gar was caught by bow-fishing, this is the way most anglers fish for this species.
The biggest alligator gar ever was caught in 1991 with bow-fishing, it weighed in at 365 lbs and measured 9'6" in length. This is still the largest confirmed alligator gar ever recorded to day! (picture of catch below)