A man been charged and a Sydney grandmother is fighting for life after she was allegedly punched in the head while she was at a park with her six-year-old grandson.

The 71-year-old woman was on Francis Street in Strathfield about 12.10pm yesterday when there was “some type of adverse reaction” with a 52-year-old man walking his dog, police said.

Superintendent Robert Toynton said a short time later a 46-year-old man, believed to be the woman’s son-in-law, arrived at the park.

“At some point, police will allege the 52-year-old has approached the son-in-law in the vehicle and has assaulted him,” Toynton said.

“Police will then allege the 52-year-old man approached the 71-year-old grandmother and with one hit has punched her in the head.

“The lady has then fallen to the ground and subsequently a short time later police and emergency services were called to that location.”

It is understood the alleged attacker and the woman are not known to each other.

The woman was rushed to Royal Prince Alfred Hospital in a critical condition and underwent emergency surgery yesterday.

“That woman is still in a critical condition,” Toynton said.

“Her condition is what I would call grave – she’s very, very unwell.

“From my experience as a police officer, this is an absolutely abhorrent attack.

“It is an unprovoked attack and it absolutely sickens us that this has happened in our community.

“But what we want to assure the community of is as police we will act swiftly, we will put all of our resources into these types of offences and we will arrest people and put them before the courts as quickly as we can.”

Police arrested a man at a home in Strathfield at 8.30am today.

The 52-year-old man was taken to Auburn police station, where he was charged with wounding a person with the intent to cause grievous bodily harm and common assault.

He was refused bail to appear before Burwood Local Court today.