When Duncan Logan decided to open his accelerator program five years ago in downtown San Francisco, he was inspired by Marc Andreessen’s maxim that “software is eating the world.”

Now, after helping launch such global juggernauts as Uber Technologies Inc. and Spotify Technology SA, he’s getting a big backer to take his business model overseas.

HNA Group, a Chinese company with holdings from aviation to financial services to real estate and logistics, has invested $336 million in RocketSpace, marking one of the largest such fundings by a China-based investor in the U.S.

It is the first money raised by RocketSpace, which was started in 2011 by Duncan Logan. The British native put $20,000 of his own money into RocketSpace, which has now housed more than 800 tech startups in an office building in San Francisco’s financial district. Alumni include Uber and 15 other tech companies valued at more than $1 billion.

The new money will be deployed quickly, and RocketSpace intends to open campuses in China and London in 2017. RocketSpace was looking to raise about $50 million, but HNA said the figure lacked ambition, and “we were taken along in their story,” Mr. Logan said.

HNA’s backing represents China’s biggest bet on an accelerator, and one of the single largest investments in a U.S. startup by a China-based group, according to data from Dow Jones VentureSource.

Under the deal, HNA is taking an undisclosed minority stake in RocketSpace, which declined to discuss the accelerator’s valuation.

Earlier this year, HNA created an arm of the company called EcoTech to step up innovation across the company.

With RocketSpace, HNA hopes to serve Chinese startups and expand to new business areas. “We are highly interested in cloud computing, big data, internet of things, and artificial intelligence,” Eric Tong, CEO of EcoTech said via email.

Mr. Logan, who worked previously in finance and then at tech companies, said he believes tech businesses will become so important that cities of the future will have a downtown tech center the way they now have a downtown financial center.

RocketSpace, which he calls “the stock exchange of tech,” could become a focal point for local tech communities and the nucleus the downtown of the future.

“I felt there was an opportunity for an organization to say, ‘We’ll be the coordinator of that ecosystem,’” Mr. Logan said.

The investment from HNA is meant to help RocketSpace expand to cities around the world and eventually to help build a stronger startup community in China. Mr. Logan said it could also provide a way for U.S. startups to get established in China and start attracting Chinese investment before their businesses get copied by entrepreneurs in that country.

In January, HNA invested in Uber’s Chinese unit as part of a funding round that valued UberChina at $7 billion.

With a population of 1.3 billion, China can see its startups get big quickly “on a scale we’d struggle to understand over here,” Mr. Logan said. He noted that Uber paid “a very high price for not opening in China and getting funding” before rival Didi Chuxing Technology Co. got going. Uber on Monday, in recognition of that competitive tension, agreed to sell UberChina to Didi.

Unlike many accelerators and co-working spaces, RocketSpace doesn’t take equity in its member startups because Mr. Logan believes that approach attracts the best startups.

Startups applying to RocketSpace are judged first by the quality of their investors—they have to be seed-funded, signaling that the founders “are no longer building a lifestyle business,” Mr. Logan said. Next comes a review of the founders’ track records and the traction of their businesses.

Once they join, in addition to getting office space, the startups can receive help with fundraising or connections to professionals like lawyers and accountants. There is also access to scores of corporate partners including Royal Bank of Scotland and JetBlue Technology Ventures.

“Suddenly innovation is a C-suite issue, like security after the Target breach,” Mr. Logan said. “…It’s symbiotic for both startups and corporates. Corporations do things that startups struggle with.”