The attack happened in the Balornock area at around 11.45pm on Friday as the 26-year-old victim was waiting at a bus stop in Wallacewell Quadrant.
A small silver car stopped beside him and a passenger in the vehicle ran towards the victim with a hammer, chasing him into the park where he was struck by the vehicle.
The two other male occupants of the car then got out and assaulted the victim with weapons.
The attackers got back into the car and drove off through Wallacewell Quadrant and along Wallacewell Road.
The victim was taken to Queen Elizabeth University Hospital where his condition is described as serious but stable.
One of the men was in his early twenties with blond hair and was wearing a red top. The other two men are described as being in their late teens to early twenties.
Detective Constable William Corkindale, from Shettleston CID, said: “This was a horrendous attack which has left the victim seriously injured and it is imperative that we trace the people responsible.
“I would appeal to anyone who was in the area around the time the incident took place, who may have witnessed what happened or saw anything suspicious, to come forward.
“We understand that the front passenger window of the small silver car involved was smashed and so I would also ask anyone who noticed a car matching this description to get in touch.