That would bring its total to 3,000 across the UK and Ireland - almost double that of closest rival Greggs, which has 1,698 restaurants.
Subway said growing customer demand for its sandwiches had driven the decision.
The firm is also in the process of  overhauling its stores with a revamped menu and a new look for the shops.
It said its expansion plans would create 5,000 new jobs.
The chain's main menu is still "subs" - long, US-style baguette-like sandwiches made with soft bread - but it also now offers salads.
Subway's UK director Peter Dowding said it was also looking at overhauling its breakfast and evening menus.
"We already have a breakfast menu, but it's a part of the day we need to work on," he said.
The firm overtook McDonald's as the world's largest restaurant chain more than six years ago, but Mr Dowding said the fast food giant was not its only competitor.
"It's everyone. It's a very competitive world out there," he said.
Mr Dowding said the chain's most popular sandwiches varied according to location, but were typically the Italian BMT sandwich containing salami, pepperoni and ham, the meatball marinara and the tuna sandwich.
He said it was "a misconception" that fast food was unhealthy, noting that six of the nine sandwiches on its core menu contained under 400 calories.
"We offer a broad range of products. We cater for choice driven by consumer demand," he added.
All of Subway's stores are independently owned and operated as franchises of the US brand, with  three-fifths of its UK and Irish outlets located on traditional high streets.
Mr Dowding said the firm had so far seen no impact from the UK's decision to leave the European Union.
"It's business as usual. Like any other business we're waiting to see what the government does and will tackle it from there," he said.
Mr Dowding joined the firm just nine months ago, but said he'd eaten at the company for the past 20 years.
"When they offered me the job I almost bit their arm off. I'm delighted to be taking their evolution forward."
Subway, which was founded in the US just over 50 years ago, now has 44,000 stores in 112 countries.
Sandwich chain Subway is planning to open another 500 stores by 2020 as it seeks to cement its place as the UK's largest High Street fast food chain.