The man was taken to Inverclyde Royal Hospital with a head injury following a disturbance in Nelson Street at about 00:50.
His condition has been described as serious.
Two other men were also taken to hospital. A 20-year-old is being treated for face and arm injuries and a 42-year-old for a head injury.
Their conditions have been described as stable.
Det Sgt Alex Allardyce, of Police Scotland, said: "At this time, extensive inquiries are ongoing to establish more details on the circumstances surrounding the disturbance.
"Officers are following a number of lines of inquiry and I would urge any witnesses, or anyone with information that may assist the police investigation to contact Greenock Police Office through 101."
Police are treating an attack on a 24-year-old man in Greenock as attempted murder.