Sainsbury's is refitting many of its stores
The supermarket reported a 6.4% jump in sales excluding petrol for the 12 week period to 5 January.
But including petrol, sales grew by only 5% because of cheaper fuel prices.
During the weeks over Christmas and New Year, its sales grew by 6.8%.
'This is the fourth quarter of increasingly strong like-for-like sales growth in the UK and the third consecutive quarter of like-for-like sales of 6.0% or more," said the company's chief executive Sir Peter Davis in a statement.
"This is a very significant improvement over the 0.6% achieved in the same three quarters last year."
'Record volumes'
Sir Peter joined Sainsbury's in March 2000 and launched a three-year programme aimed at getting market share back from Tesco.
It has embarked on a comprehensive store refurbishment programme, something it said which helped contribute to "record volumes" being delivered to stores on peak days over the Christmas period.
Sainsbury's used to be the UK's largest retailer until Tesco overtook it in 1995.
But Sir Peter said Sainsbury was now beginning to take customers back from its arch rival.
"We're very encouraged by these results, which gives us confidence that we are on track to fulfil the targets we have set ourselves this year and to deliver a sustainable recovery of the business," said Sir Peter
Despite the upbeat statement, shares in Sainsbury slipped back in early London trade, falling 4.5p to 368p.