The Port Authority wants to ease overcrowding at its bus terminal with a $400 million garage.

The project, called the Galvin Plaza Bus Annex, would be a one-floor enclosed garage built on a Port Authority-owned vacant lot on West 39th Street between 10th and 11th avenues, according to agency spokesman Chris Valens. The facility would be able to hold 100 buses and let them connect between the terminal and the Lincoln Tunnel. The project is estimated to be complete in 2020.

When there is a backup in the terminal, "we end up diverting buses away from the terminal, they end up on city streets waiting for their turn to get into the bus terminal," Valens said.

He added that the garage would act like staging area to bring buses into the terminal as needed.

The project is included in Gov. Andrew Cuomo's $4.9 billion transportation resiliency plan submitted to the Federal Transportation Administration, which has made $3 billion in federal funds available for the region's transportation systems. The bus annex project is eligible for $230 million of that federal money.

The extra space could help if another storm knocks out ways in and out of Manhattan. During Superstorm Sandy, the Lincoln Tunnel was the only open traffic tunnel into the city.

"We find that bus service has been the most resilient mass transportation when some of these storms hit," Valens said. "This will allow us to handle those extra crowds."