Four people have been taken to hospital after a crash on the Sydney Harbour Bridge, just minutes after two people fainted doing the Bridge Climb.

An accident between a Forest Coach Lines bus carrying 20 people and a car closed two southbound lanes just after midday today.

Three people in the car were taken to Royal North Shore Hospital in a stable condition, and one bus passenger was taken to St Vincent's Hospital.

All southbound lanes are now open, but a spokesman from the Transport Management Centre said traffic was still heavy.

Earlier today, lane seven of the bridge was closed twice in an hour when two people fainted doing the Bridge Climb.