Police said the man got into a black Honda Civic following an argument at a house party just before 10pm on Saturday.
The car mounted the kerb on Elizabeth Drive and was in collision with a brick wall before hitting two men, aged 37 and 54.
A 39-year-old woman was also injured when she was attacked by the driver as she attempted to stop him leaving the scene.
The Civic left and then returned, striking a third man, aged 30, who suffered facial injuries. It then left the scene.
No-one was seriously injured in the incident.
Detective Inspector Dave Watts of Wakefield CID, said “We have a number of active enquiries ongoing today into what has quite clearly been a very serious incident in Castleford on Saturday evening.
“It is extremely fortunate that no-one was seriously injured in what have must been a very frightening experience for everyone present.
“I would like to speak with anyone who witnessed or has information about took place, who has not yet come forwards.
“We would also like to speak with anyone who has information about the car involved, a black 08 plate Honda Civic.
“Anyone who has information is asked to contact Wakefield CID on 101 referencing crime number 13180333185.
“Information can also be given anonymously to the independent Crimestoppers charity on 0800 555 111.”