Los Angeles residents call the urban runoff that flows through their concrete storm drain the Los Angeles River. But the euphemism hasn’t fooled property owners.

Riverfront property is premium real estate in many cities. Yet property along the 51 miles that snake through downtown from San Fernando to Long Beach is largely a mix of warehouses, power lines, tow yards and concrete—lots of concrete. When homes have been built along it, they have been designed to look the other way.

But a project by Los Angeles-based developer Rick Rosenberg and designed by architect Stephen Albert is reframing the liability as an asset.

Mr. Rosenberg, president of Metric Holdings Inc., hopes to convert a 2.5-acre riverside parcel that now houses a parking lot and an abandoned auto dealership into a six-story, mixed-use building with 7,691 square feet of retail and 254 apartments. If approved by city’s planning commission, the property, located in the community of Reseda, would bear little resemblance to almost anything that has been built along the river since the U.S. Army Corps of Engineers began paving it in the 1930s.

Instead of hiding the river, Mr. Rosenberg’s development embraces it, imagining terraced apartments and retail facing a flowing river with a bike path along greener banks.