Elon Musk's Boring Company has presented plans to build a Hyperloop tunnel under Culver City, California.
The plans were presented at a council meeting on Monday by Jehn Balajadia, operations co-ordinator of the firm.
She said: "The purpose of Boring Company is to alleviate soul-destroying traffic and augment public transit."
Mr Musk, also chief of Tesla Inc and Space Exploration Technologies Corp, didn't speak at the meeting.
A report by the Culver City manager's office stated: "The Boring Company has proposed a privately funded human transportation tunnel that would run underneath the Westside of Los Angeles.
"The tunnel would contain a high-speed underground public transportation system in which passengers are transported on autonomous electric skates travelling at 125-150mph."
The electric skates will be designed to carry either single passenger vehicles or what are described as "mass transit" pods capable of transporting between eight and 16 people.
The company says the plan would ease road congestion and allow people to move around the city more easily.
Ms Balajadia stressed that the company was not looking for public funding and that the cost to passengers would be comparable to, or less than existing forms of public transit in the region.
Mr Musk, who himself lives in Bel Air, is reported by Bloomberg to have first mooted the idea of a tunnel system back in December 2016, when he tweeted that he was fed up with LA traffic and would "build a tunnel boring machine".
The proposed route is from the headquarters of Musk's company SpaceX in Hawthorne to West Los Angeles passing underneath Sepulveda Boulevard through Culver City.
The plans are reported to have been well-received by some members of the council as a way of dealing with the region's traffic congestion.
However, concerns were expressed by council member Meghan Sahli-Wells about a private company creating a system that may compete with existing public transport agencies in Los Angeles.
"This is really seductive," said Ms Sahli-Wells. "It looks super-sexy and super-easy, but it's half-baked from a public perspective."
As reported on the BBC last July the serial entrepreneur also tweeted his interest in building a Hyperloop on the East Coast.
When asked for further details on the claims in his tweets, a spokesperson for the firm told the BBC: "The Boring Company has had a number of promising conversations with local, state and federal government officials.
"With a few exceptions, feedback has been very positive and we have received verbal support from key government decision-makers for tunnelling plans, including a Hyperloop route from New York to Washington DC.
"We look forward to future conversations with the cities and states along this route and we expect to secure the formal approvals necessary to break ground later this year."
At the time, the company said that it was expecting to start digging by the end of 2017.