The victim was assaulted by another man in an unprovoked attack as he walked in Bath Street, near to Wellington Street, at about 9.45pm on Friday.
He was taken by ambulance to Glasgow Royal Infirmary with a serious head injury.
Police are searching for a suspect described as around 6ft, wearing a grey three-quarter length coat with a white shirt, brown shoes and facial stubble.
He was last seen on Sauchiehall Street at the junction with West Campbell Street.
Detective Inspector Peter Sharp appealed for anyone with information to contact Police Scotland.
He said: “To carry out an unprovoked attack on an elderly man is despicable and cowardly.
“This assault has left a 77-year-old man in a critical condition and a family traumatised by what has happened. It’s imperative we trace the man responsible.
“I would like to the thank members of the public who have already contacted us with information, however, we know there were other people in the area who have yet to speak to us and I would urge them to get in touch.
“We all have the right to go about our daily business without being subjected to violent acts.”
Police said the suspect was with a woman before the attack, who is described as blonde and of medium build.
She was wearing a long brown coat and a leopard print top and carrying a brown handbag.
Officers are reviewing CCTV footage from the area in a bid to glean more information on the suspect.