The Virgin Media Business contest offers £1 million of cash, marketing and mentoring to small and medium sized companies either just starting up or looking to expand.
The business broadband giant is hoping that 5,000 firms will enter the so-called VOOM 2016 contest, twice as many as last year.
Sir Richard told the Press Association that he still remembers the £300 his mother gave to him to start his career in business, without which, Virgin may never have been launched.
The competition was offering a "golden ticket" to help take an idea onto a global stage, he said, adding: "If you have an idea to make other people's lives better, screw it, just do it.
"Britain has been behind with tech businesses, so it would be great to have some real cutting edge technology firms coming forward."
Entrants will receive tips and mentoring throughout the competition ahead of the winners being announced in June.
One of last year's winners, Jeff Paterson, said his automated kiosk business, turning foreign currency into British notes and coins, had taken off since last year - with daily calls from potential investors.
Gem Misa, founder of Cauli Rice, has seen her gluten-free rice stocked in more than 1,000 supermarkets since being a finalist last year.