This is the man police believe methodically smashed the Kokoda Track war memorial in Sydney in a "strategic operation" that will cost up to $40,000 to repair.

The board of the Kokoda Track Memorial Walkway at Rhodes said the man's destructive rampage with a spray can and a blunt object lasted a few hours on Friday night or early on Saturday.

Police said the vandal appeared to have put a lot of thought into the "strategic operation", wearing gloves and making sure his face was partially covered with a grey or white hooded jumper while he took to 15 of the 22 individual stations that make up the memorial.

"He's just gone in and smashed the whole place up ... like an ant at work," one officer, who asked not to be named, said.