UK stocks of the product sold out in 36 hours and Van Meuwen is filling 10,000 more packets to meet demand.
Thompson & Morgan brand Van Meuwen says the tomato can grow to 3lb.
Van Meuwen general manager Chris Wright said: "We initially launched 500 packets of Gigantomo seeds.
"This may not sound like a vast number but in the world of horticulture it's an impressive feat - last year our best selling tomato 'Tomazing' picked up 507 sales for the whole of the year.
"We couldn't believe it when our entire stock of Gigantomo packets sold within 36 hours of the variety being launched.
"We knew we were on to a winner when we negotiated the exclusive UK supply of Gigantomo seeds and plants, but initial interest and sales have exceeded all expectations.
"It's a bold jump up to 10,00 packets but based on the speed of initial customer uptake and the level of web traffic we have received for Gigantomo seeds it may be that even this won't be enough to meet demand.
"It seems it's not just our customers that can expect big things from this tasty giant tomato in 2015.
Simon Crawford called in five years ago to finish the work of late American grower Paul Thomas, who spent 15 years trying to breed the huge tomato.
Gigantomo, can reach over 6ft tall, producing fruits up to 10 inches wide and as heavy as 3lbs. It was first launched in the US last year as SteakHouse. Van Meuwen is the sole UK supplier but EU chiefs ruled the name unacceptable so it was changed to Gigantomo.
Gardeners can take tomatoe to the Harrogate Autumn Flower Show (18-20 September) and take part in the National Gigantomo Championships.Van Meuwen is offering a top prize of £1,000 for the heaviest fruit, with a further £5,000 jackpot up for grabs if it also breaks the world record of 7lbs 12oz.
Six seeds are £3.99 or order plug plants are five for £14.99.