Morrisons is the latest of the big supermarkets to engage in a price war at the petrol pumps.
Drivers will get 6p off a single litre of petrol if they spend more than £40 on groceries in the store.
Morrisons' 'Fuel Britannia' campaign undercuts similar offers from the Co-op and Sainsbury's.
The Co-op gives 5p off a litre when customers spend £30 or more and Sainsbury's 5p off a litre if shoppers part with £50 or more.
Tesco's 5p for £50 offer expired a few weeks ago but a spokesman from the supermarket giant hinted another offer may be announced.
Good news for customers
Fuel is now the largest single contributor to the cost of living for households in the UK, according to the Office for National Statistics.
Vicki Burn, spokesperson for the RAC, says the campaign is good news for shoppers who already use the supermarket and as the Morrisons deal is 6p a litre, instead of the usual 5p, this deal is "better than most".
But, she says, it is vital people shop around for the best deals and use comparison websites like petrolprices.com. She advises drivers to be especially wary of filling up at motorway service stations because of the "exorbitant" prices they charge.
Customers need to spend £40 at Morrisons to get a 6p coupon though there are exemptions including fuel, cash back, tobacco, dry cleaning and photo printing.
Richard Lancaster, marketing director at Morrisons, says with petrol prices at an all-time high and disposable income down £100 a month from last year, the supermarket wants to provide customers with the best deal on the market.
"We know over the Easter holidays and the Royal Wedding, motorists will want to travel further to visit friends and relatives, but will be put off by the cost of petrol. Our offer ensures our customers can enjoy this time and worry less about the cost," he adds.
Read: Save £500 on your petrol bill
How you can cut down on fuel costs
In March petrol hit a new record average of 130p per litre, and although it's impossible to do anything about rising costs, there are ways you can save money.
* By changing driving patterns you can cut down the amount you spend. Driving at a constant speed, making sure you're not carrying around unnecessary weight, like unused roof-racks, keeping your tyres at the right pressure and driving below the speed limit will cut down petrol costs.
* Making several small journeys is costly, as your engine won't have enough time to warm up properly.
* Plan your route before you leave the house and try and combine journeys.