Asda said that from today it was cutting prices by up to 2p a litre.
The company added that those filling up at Asda would pay no more than 130.7p a litre for petrol and no more than 135.7p a litre for diesel.
The move follows the announcement that rival supermarket Tesco was cutting the cost of 3,000 products as part of a £500 million campaign.
Asda said it was responding to the drop in wholesale fuel prices.
The company’s petrol trading director, Andy Peake, said: “We know the price of petrol matters to our customers which is why we aim to be the first to pass on cuts in the cost of crude. That’s again what we’re doing today.”