A Midcentury architectural house in Los Angeles built for the guitarist for 1960s rock group The Doors has hit the market for $13.99 million after a gut renovation.

Robby Krieger, 72, commissioned the single-story hexagonal mansion in Bel Air in the late 1960s. He lived there with his family though the 1970s, when it served as a watering hole for the rock ‘n’ roll scene of the time. The unusual property, which has no right angles, hit the market on Thursday following a two-year restoration that put a contemporary spin on its ’70s style.

Despite its celebrity cache, the home had fallen into disrepair and was on the brink of demise when current owner Adam Bold, founder of private equity firm Superbrands, toured the property in 2016, he said.

The home was stripped to the studs and renderings of a “two-story, square mcmansion” were on display, Mr. Bold said. “They were pitching it as a development opportunity.”

“I thought it would be a shame because it’s such an architectural treasure,” he said. Mr. Bold ended up buying the property for $5.2 million, according to property records.

His vision was to restore the home to a 1970s style that would still appeal to modern buyers.

He kept one of the last remaining interior details from Mr. Krieger’s time: a Brutalist-style frieze the rocker commissioned of the band, which hangs over a 10-foot-wide fireplace.

He’s also retained the original blue-tile roof, which “looks like Spanish tile but is actually from Japan,” Mr. Bold said. “It’s very ’70s but now retro cool.”

Diego Monchamp, an interior designer with Brown Design Group, said it’s one of the most unusual Midcentury homes on the market.

“What I’m seeing on the market are boxes on top of boxes that are askew a little. They are all a little bit the same,” said Mr. Monchamp, who handled the redesign. “It’s not like that.”

Mr. Krieger commissioned the home from local architect Matthew Leizer, who also designed the Santa Monica Library, and built the musician’s Bel Air home with no right angles.

The interior architect honored the 1970s theme by laying down textural terrazzo flooring. “It’s a material you would have seen in airports and banks and very high-end homes of that era,” Mr. Monchamp said.

They also used unfinished solid maple for all of the wood detail, including the kitchen cabinetry, and relaid panels of cork in the ceiling to help with the harsh acoustics of the open floor plan. Glass walls cover the exterior of the home and those facing the interior courtyard.

Mr. Bold learned that Mr. Krieger wasn’t the only rocker to live at the house, which was also home in the 1990s to Fred Durst, lead singer of Limp Bizkit.

“That was back when he was dating Britney Spears and Christina Aguilera,” Mr. Bold said. (Both singers have denied having relationships with Mr. Durst.)

The privacy celebrities crave has been part of the lure of the property, which spans near one-and-a-half acres, said Sacha Radford, who is listing the home for The Agency.

“There’s total privacy all the way around the lot,” she said.

The next owner will also get the pleasure of owning a home that was frequented by all the great musicians of the 1970s or “anybody who was anybody,” Mr. Bold said. “I wish the walls had cameras.”