John Dugdale pleaded guilty to GBH after pushing grandfather Paul Eva against a brick wall, leaving the pensioner with a broken wrist, nose and cheekbone.
Police released CCTV footage of the incident, showing the car stop in front of Mr Eva, who is seen talking to the driver before walking away.
Dugdale then pulls the car over and chases after Mr Eva on foot, clearly pushing the pensioner over from behind and into a wall.
He was sentenced on Tuesday at Croydon Crown Court.
The pensioner was walking with his wife along Parish Lane in Penge from his daughter's birthday at about 7.50pm on April 21 when he exchanged words with Dugdale, who was driving his car.
As he walked away, Dugdale parked his car, with his 16-month-old granddaughter sat inside, and went after Mr Eva on foot.
He then pushed Mr Eva from behind into a wall with such force that his wife thought he may have been dead.
Mr Eva was found unconscious by paramedics.
Speaking after the sentencing, Mr Eva told ITV News: "I hadn't have seen the CCTV... I had no idea what had happened he just treated me complete contempt."
Asked if he had received any apology at court, he said: "No, he just wouldn't even look at me, I don't think he was at all apologetic. He was just sad that he got caught."
Video report by ITV News Correspondent Richard Pallot
Dugdale claimed he was afraid for the safety of his 16-month-old grandchild.
He fled the scene immediately and ignored the screams of Mr Eva's wife.
"At one point I looked down at him when he had hit his head on the wall , I mean I actually didn't think he was alive anymore, it was horrendous.
"His face was completely mashed up."
The court heard how Dugdale has a previous conviction for threatening a delivery driver with a rounders bat for simply parking across his drive for five minutes.
In sentencing for the latest incident, the judge said: "Well what a lesson to teach your young granddaughter, who in your own submission was watching on."