A Bel Air, Los Angeles, villa built for old Hollywood stars John Farrow and Maureen O’Sullivan—the parents of actress Mia Farrow–has hit the market for $5.785 million.

Farrow, an actor and filmmaker who won an Academy Award in 1957 for best screenplay for “Around the World in 80 Days,” and O’Sullivan, who played Jane in the first film adaptation of the Tarzan story, built the lushly landscaped Mediterranean-style house in lower Bel Air in 1937. The home hit the market on Monday with Joy Denton, Peter Martocchio and David Goldberg of Sotheby’s International Realty.

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The cream-colored home with its red tile roof spans roughly 4,250 square feet, including five bedrooms and four full bathrooms.

The back of the home slopes down a lushly landscaped hillside with walking paths, old trees and shaded gardens, according to images from the listing.

“This property is in an A-plus location in lower Bel Air and offers incredible privacy,” Ms. Denton told Mansion Global.

Farrow and O’Sullivan owned the home for several years, Ms. Denton said. They moved there in 1937, the year after they were married.

The home has an attached two-car garage that abuts a home office, a configuration Farrow used in his filmmaking. He cut a hole between the two spaces as a way to project movies into his office room from the garage, Ms. Denton said.

Later owners sealed the holes, but the home still has many of its original details.

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From the street level, it opens onto the second-floor communal spaces, including a living room with a vaulted ceiling, fireplace and open kitchen.

Balconies wrap the back of the house overlooking the gardens, pool and half-an-acre of grounds, and a room used as a music studio now could be converted back into a bedroom, according to the listing.

The current owner, composer Bruce Broughton, who wrote the scores to a number of Disney classics including “Homeward Bound,” bought the house in 1997 for $1.6 million, according to property records. He did not immediately return a request for comment about the home.