Sales for the 12 weeks ending May 22 rose 7.8% on like-for-like basis in the UK. Overall sales rose 12.3% in the quarter.
Tesco has continued to add more clothes to its range and has dedicated more space to non-food items such as DVDs.
According to reports the company has said it will cut the price on many goods by £70m to maintain its lead against its rivals.
In a statement chief executive Sir Terry Leahy said: "I am particularly pleased that our core UK food business has continued to grow market share and to perform very strongly in the first quarter."
Tesco's share of the grocery market climbed to 27.6% in the 12 weeks ended May 23 from 27.5% a month earlier.