City Council members approved the $4.8-billion package of renovations by a vote of 10 to 3.
Opponents say they're skeptical of the airport's safety claims that the updated runway would better accommodate larger, modern planes, like the A380 Airbus. The northernmost runway will be moved about 260 feet closer to the Westchester and Playa del Rey neighborhoods.
Congresswoman Maxine Waters cited a NASA study saying moving the runway isn't necessary.
"The north airfield of LAX is extremely safe under the current configuration," she said. "I thought this conclusion would put to rest the talk of moving the north runways closer to homes (and) businesses in Westchester. Unfortunately, I was wrong."
Most of the opposition to moving the runway has come from some of the neighborhood councils located near the airport.
"We want to incorporate safety enhancements that do not require movement of runways," said Marc Saltzberg of the Venice Neighborhood Council. "We want to reduce freeway traffic and discourage traffic flow into local neighborhoods while avoiding any new Lincoln Boulevard connection tunnels."
Business and labor led the support for moving the runway.
"It will make Los Angeles airport safer, contrary to what's been said," said Alan Rothenberg of the Los Angeles Area Chamber of Commerce. "More efficient, more competitive. It will take no homes, it will take no businesses."
The project would also create a transportation station to connect LAX to a light rail service, consolidate its rental car facility and install an elevated people mover.
The plan now goes to the Los Angeles County Board of Supervisors and Federal Aviation Administration officials for consideration.