However, the like-for-like rise, excluding VAT and petrol, is lower than the 8.4% increase it reported in the previous quarter.
Asda chief financial officer Judith McKenna has largely attributed the slowdown to a drop in food inflation.
TNS Worldpanel data also reveals that its market share rose to 17% in the 12 weeks to 12 July, up from 16.7% in the same period a year ago.
By comparison Tesco holds a 31% market share, while Sainsbury’s has 16%.
Asda, the second-largest supermarket chain, claims to have attracted more customers by broadening its appeal, lowering prices and improving product quality.
Its food, home, leisure and clothing range performed particularly well.
Asda is also offering consumers a range of recipes to feed the family for £4. It mirrors Sainsbury’s own Feed your Family for a Fiver campaign.
This year, Asda has opened ten new stores which it claims are performing above expectations.
McKenna says: “Consumers continue to be somewhat cautious, with many people choosing to use any extra money they have to pay down debt and save more.
“This is not going to be a straight line economic recovery, however, in this environment, we are well placed to continue gaining market share by giving customers what they want.”