Kevin Spacey, 50 Cent, Carmelo Anthony, Kyrie Irving and Target are backing Casper, helping the sleep start-up close a $170 million Series C investment round.
Founded in 2013, Casper sells mattresses and other sleep products directly to consumers and at stores and offers shoppers an extended 100-day return policy.
"We think we're the next great consumer brand," CEO Philip Krim told CNBC's "Squawk Box" on Tuesday.
"Since the beginning, we've always thought about offering products both online and offline, focusing on digital first," Krim said. Casper also sells products at Target and home-furnishing companies like West Elm.
These have been the "key ingredients" that have helped Casper accelerate its business so quickly, Krim said.
Casper said its total funding is now $240 million.
Krim doesn't rule out an initial public offering, either.
"We think we are set up to do well in the public markets," he said when asked about a possible IPO. "We think we can continue to accelerate what we're doing, and that will give us the position to be public when we like."
Tony Florence, a general partner at New Enterprise Associates and an early investor in Casper, told CNBC he put additional money into the start-up because it is only 4 years old and is set up for capturing a significant market share.
"[Casper is] still in the early days of innovation," said Florence, whose investments include Jet.com, which was bought by Wal-Mart, and Quidsi, which was acquired by Amazon in 2011. "It's a massive market."
"Getting the word out and building awareness is the biggest barrier" today, Krim said. Investments by celebrities such as Spacey and Anthony have helped, he added.