Police said a silver Vauxhall Corsa containing three men crashed into a fence and a lamp post on Moor Road, Hunslet, just after 3.30am on Monday January 1.
The Corsa ended up in the park area on the opposite side of the carriageway.
A 33-year-old man, who was the rear seat passenger,received serious injuries and was taken to Leeds General Infirmary for treatment.
The driver, a 23 year old man, was arrested on suspicion of drug driving.
Any witnesses to the incident or the manner of driving prior to the collision is asked to contact the non-emergency number 101.