Bare-handed and without a harness, Robert climbed the 68-storey Cheung Kong Center in Hong Kong's main business district on Friday morning in hot and humid conditions.
During the climb, he attached a banner featuring the Hong Kong and Chinese flags, as well as two hands shaking.
The 57-year-old adventurer, known for climbing tall buildings worldwide, said his stunt was an "urgent appeal for peace".
"Perhaps what I do can lower the temperature and maybe raise a smile. That's my hope anyway," Robert said in a media statement prior to the ascent.
His stunt met with mixed reaction online.
"Do you really want (to) shake hands with butchers and dictators," tweeted Australia-based Chinese dissident artist Badiucao.
"This shows many foreigners don't understand the underlying issue between Hong Kong and China," another user wrote on a popular forum.
Spectre of Tiananmen
Hong Kong has been rocked by 10 weeks of huge, sometimes violent, democracy protests.
They were sparked by opposition to a plan to allow extraditions to the mainland, but have since morphed into a wider call for democratic rights.
Watching the Hong Kong protests from afar, Chinese dissident-artist Ai Weiwei on Friday, warned of a repeat of the 1989 Tiananmen Square crackdown in Beijing.
"I don't think any prediction is too big," the 61-year-old told AFP in an interview in his Berlin studio.
China "is a society which sacrifices anything to maintain its control," he warned.
From April 15 to June 4, 1989, Chinese troops and tanks fired at demonstrators on Tiananmen Square, protesting against inflation, government corruption, and restrictions on freedom of speech and political participation.
Estimates of the death toll vary from several hundreds to several thousands, with thousands more wounded.
Robert's climb comes as more mass demonstrations are expected at the weekend.
China has likened the increasingly violent protests to terrorism and warned it could use force to quell them.
Later on Friday, the boss of Hong Kong carrier Cathay Pacific Airways quit, the highest-profile corporate casualty of unrest roiling the former British colony, after Beijing targeted the airline over staff involvement in mass protests.
The abrupt departure of Chief Executive Rupert Hogg, a move the company said was “to take responsibility ... in view of recent events,” shows just how much pressure Beijing is piling on corporate giants and the city as it seeks to snuff out the protests.
China took over the former British colony in 1997 under the framework of “one country, two systems”, which protesters today fear is being eroded.