Safeway's new chief executive, Carlos Criado-Perez, said that shoppers did not think the cards offered value.
The decision is in contrast to the prevailing view which has seen loyalty cards become a key weapon in the battle for customers between the UK's four big supermarket chains.
Customers build up points on the cards related to the amount they spend, which can be converted into money off purchases.
Tesco, which was first to launch such a card, was seen to have pulled off a masterstroke, especially when an initially sceptical Sainsbury's later launched its own version.
In addition to offers to customers, the cards give the shops a hitherto-undreamed of level of knowledge about individual customers and shopping habits.
Tesco, the UK's largest supermarket chain, has 14 million cardholders and says there has been no fall off in their popularity - blaming the way Safeway's was run for its lack of popularity.
Sainsbury's also said there had been no dip in their popularity, saying it was still receiving 40,000 card applications a week, with 17 million issued in total.
But rival Asda, which had run a pilot loyalty card scheme for three years, decided to scrap it last August.
It said that a recent consultation with customers had seen just five out of 5,500 raise a desire for a loyalty card.
Mr Criado-Perez said that scrapping Safeway's ABC loyalty card scheme would save it £50m this year, money which it would invest in cutting prices.
Facing stronger competition
"People have lost interest in (loyalty card) points and don't think they give value," he said.
"What they really appreciate are straightforward product offers at great prices."
Safeway said its "Best Deals Ever" programme had encouraged 750,000 customers to switch to it since October.
Some £30m was invested in the price cutting initiative in the six months to March 2000, with this figure being increased to £110m in the current financial year.
Safeway's profits and stock market value have fallen sharply in the face of tougher opposition from its existing rivals, Tesco, Sainsbury's and Asda.
Competition has been particularly fierce since Asda was bought by US giant Wal-Mart last year.
Incentives for stores
Mr Criado-Perez, a former Wal-Mart executive, has attempted to breath fresh life into the chain by devolving promotion and price decisions to individual stores, with bonus incentives for good performance.
The trading performance he outlined on Thursday shows the amount of work needed, with Safeway expecting pre-tax profits of about £245m ($383m) for the year just ended.
Although that was towards the top end of forecasts, it was still a long way short of the £350m made the year before.
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