The supermarket will test the service at three stores and plans to expand it to 30 outlets by Christmas.
Amazon recently raised the pressure on UK supermarkets with the launch of same-day deliveries in London.
The online retail giant signed a deal with Morrisons and now sells 130,000 products, including fresh goods.
Sainsbury's stores in London's Streatham Common, Richmond and Brookwood in Surrey will try out the service which will allow people who order their shopping by 12.00pm to receive their goods within six hours.
At present, customers have to order the day before to receive their shopping.
Britain's second largest supermarket group said: "Assuming the trials are successful, same-day online grocery delivery will be available in 30 stores by Christmas."
The UK retail sector has been under growing pressure to retain and build customer numbers as more shoppers have turned to discount supermarket chains Lidl and Aldi.
Recent figures from analysts Kantar Worldpanel showed that total supermarket sales fell in the three months to 19 June. The combined market share of Aldi and Lidl hit a record high of 10.5% with both reporting rising sales. In contrast, the big four - Tesco, Sainsbury's, Asda and Morrisons - all reported falling sales during the period.
The online grocery business is forecast to be worth Â£9.8bn by the end of this year, according to market analyst Mintel, and could grow to Â£15bn by 2020.
Sainsbury's is hoping a new distribution centre in Bromley-by-Bow in east London will help "enable its customers to shop whenever and wherever they want and will cater for the growing demand in the capital for Sainsbury's online groceries service".
The company is looking to fill 470 jobs at the centre which will open in the autumn. It hopes to recruit a further 430 people by 2020.
Sainsbury's is ramping up the fight for a bigger share of the online grocery market by launching a same-day delivery service.