While official confirmation is still pending, Mr Baker's tuna is thought to be the heaviest to be caught on rod and reel. It took him just 40 minutes to land the monstrous fish, using 60kg of gear.
He finally got the tuna up onto Enchanter Fishing Charter's Cova Rosa about 3am. It will now be weighed, measured and Mr Baker's gear will be checked before a JP can sign and verify the catch.
It is estimated a tuna of that size would be worth up to $70,000 on the Japanese market. However Mr Baker has another plan - to hang his trophy proudly on the wall.
Cova Rosa skipper Lance Goodhew said the catch was "amazing" and "world class".
According to the International Game Fish Association's records, the largest bluefin tuna caught was 678.58kg, landed in October 1979 in Nova Scotia, Canada, by Ken Fraser.
The world record for the biggest fish caught with a rod and reel, until this weekend, was about 25kg less than Mr Baker's tuna.
Kevin's tuna
* Northern pacific bluefin tuna.
* Weighed 352kg.
* Took 40 minutes to catch off Greymouth coast.
* Landed at 3am.