In a video released today, the charity appealed for witnesses who have may have seen the attack take place.
In the footage you can see the man approaching the frightened dog at the side of Jex Road, in Norwich, after 1:30pm on 9 February.
As he approaches the dog – thought to be a bulldog breed – he goes to put a lead on it as it cowers in the gutter. He waits for a woman to talk past on the other side of the road before unleashing four blows to the animals head.
The RSPCA launched a search for the dog, and its owner, today as they fear for its welfare.
“You can clearly see the dog being punched in the head with some considerable force, several times,” RSPCA inspector Laura Sayer said.
“The dog shows clear signs of fear and we are very concerned about his or her welfare
"We urge anyone with any information about who this man might be, and where he and the poor dog might be.”
Anyone with information can contact 0300 123 8018 anonymously.