Homeless man critical after Sydney assault

A homeless man is fighting for life in hospital with head injuries after he was allegedly pushed over by another man in inner Sydney.

The 50-year-old was knocked backwards, striking his head on the footpath, at Tom Uren Square in Woolloomooloo in the early hours of Monday, police say.

A 45-year-old man has been arrested at a nearby hostel and charged with recklessly inflicting grievous bodily harm.

He's been refused bail and is due to face Central Local Court on Wednesday.