The victim, who is in his 40s, managed to drive a short distance to an address on Harehills Lane where police attended shortly after 6pm yesterday.
He was treated by paramedics and taken to hospital with what are believed to be non-life-threatening injuries.
Police are appealing for witnesses to the robbery on Lupton Avenue.
The man had been threatened while he was standing by his car by a group of suspects.
They tried to steal his car keys, before opening a door and making off with the computer. But when he gave chase he was attacked from behind with what is believed to be a large knife.
The incident was one of two stabbings in Harehills yesterday evening - around 7pm on Cowper Road a man in his 30s suffered serious facial injuries following a stabbing.
Detective Inspector James Entwistle of Leeds District CID said; “I would appeal to anyone who may have been in the area and seen or heard anything suspicious around the time of the incident, or who witnessed any part of the robbery itself to come forward with any information.
"Enquiries are ongoing.”