From today customers at Asda's 196 filling stations will pay no more than 127.7p a litre for petrol and no more than 132.7p a litre for diesel.
Asda said this was the lowest price for a litre of fuel since February 2011.
The latest cut means Asda has shaved 14p off the cost of a litre of fuel since the end of April, reducing the cost of filling up a family car by almost £10.
It comes after the AA said it believed Transport Secretary Justine Greening's calls for fuel price transparency may have helped contribute to a more rapid price fall.
Sainsbury's said it was also reducing its prices, with petrol and diesel coming down by up to 2p per litre.
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