Police are appealing for witnesses after the crash in Rodley at around 2.50pm yesterday.
It happened at the junction of the A6120 Horsforth New Road and Calverley Bridge, and involved a grey Yamaha motorcycle and a blue Vauxhall Corsa.
Officers said that the motorcyclist, a man in his 20s, suffered "potentially life threatening" injuries and is receiving treatment at Leeds General Infirmary.
Police are keen to speak to anyone who witnessed this collision or who may have seen the motorcycle immediately before it.
West Yorkshire Fire and Rescue Service said that two people were trapped and two crews were called out.
The people were extricated by fire service staff and left in care of paramedics.
Staff from Rawdon and Stanningley fire crews attended the scene.
Anyone with information is asked to call Sergeant Steve Suggitt in the Eastern Area Safer Roads and Neighbourhood Support Team via 101, quoting log 1042 of November 19.