One of the earliest investors in the internet expects that bitcoin and other cryptocurrencies will be the primary means of payment in five years.

"In five years you're going to walk in and try to pay fiat [a government-backed currency like the U.S. dollar] for a Starbucks coffee, and the barista is going to laugh at you, because they're going to say, 'What is this? Are you counting out pennies? Give me shells?' venture capitalist Tim Draper said Tuesday on CNBC's "Fast Money."

"They're not going to use fiat. Five years from now, none us of will be," Draper said. "Because all of this engineering effort, all that excitement, this focus is really on bitcoin and all of the cryptos around it. And I think that's what we're all going to be using and paying with."

Starbucks' Executive Chairman Howard Schultz has hinted in the last two months about how the company may use the blockchain technology behind cryptocurrencies for a consumer payments application.

"I think blockchain technology is probably the rails in which an integrated app at Starbucks will be sitting on top of," Schultz said last week on Fox Business, echoing remarks from a January conference call.

Draper has invested in Skype and Tesla, and is a founding partner of leading venture capital firms Draper Associates and DFJ. He bought nearly 30,000 bitcoins in a 2014 U.S. Marshals Service auction. He told CNBC in December he was still holding all those coins. If that is still the case, Draper's holding is worth $322.5 million at Tuesday's bitcoin prices.

"This is the most excited I've ever been as an investor, and I was right there at the beginning of the internet," Draper said Tuesday.