It was unclear if the five people aboard the single-engine, home-built plane were related, said San Diego Fire-Rescue Department spokesman Maurice Luque. No one was injured on the ground.
The woman killed was in her late 40s and the three children are believed to be between 7 and 11 years old, said Luque, who didn't know the man's age.
Gregory B. Crane, who was aboard the plane, was listed in critical condition Monday night at Sharp Memorial Hospital, said hospital spokeswoman Alicia Cresap.
The three children were taken to Rady Children's Hospital in San Diego, Luque said.
The pilot took off from San Diego's Montgomery Field and radioed that he had an open door and was going to try to return, said Ian Gregor, a spokesman for the Federal Aviation Administration. The plane was headed for Fullerton Municipal Airport.
The plane crashed around 12:45 p.m. near the 11th hole of the Admiral Baker Golf Course in the city's Tierrasanta area.
"We saw it start to get lower and lower as it flew over, like they were trying to find a place to land it," said Tyler Monroe, assistant manager of the pro shop. "It hit the power lines."
About a dozen golfers were within about 200 yards of the crash, Monroe said, and about 100 people were on the course.
The experimental aircraft was built in 2007 and is registered to Crane of Mesa, Ariz., according to the FAA.
The FAA and the National Transportation Safety Board will investigate the cause of the crash.