Sir Bob, 61, based his miserable prediction on the effects of climate change.
“The world can decide in a fit of madness to kill itself,” he told a group of youngsters at a summit in Johannesburg, South Africa.
The former Boomtown Rats singer also warned “the next war will not be a World War One or a World War Two, it will be the end.”
He added: “We may not get to 2030. We need to address the problem of climate change urgently.”
Sir Bob is best-known for his attempts in helping to fight famine in Africa, staging Live Aid at Wembley Stadium in 1985.
He finished his speech by apologising for being “bloody miserable”, but added: “just get on with it”.
Despite the dire warnings on climate change, it emerged last month that a million square miles of Arctic seas have frozen in the past year as a new environmental trend takes hold, dubbed “global cooling”.
The extraordinary “reverse” of global warming has led to a 60 per cent rise in ice-covered ocean. Just six years ago, some scientists were predicting that all of this ice would have melted away by 2013.
The big chill has persuaded some experts that temperatures will keep falling for decades and throws fresh doubts on claims that global warming will devastate the planet.
Details of the latest twist in the debate emerged in a secret memo to the United Nations Intergovernmental Panel on Climate Change.
It says that a chillier-than-usual summer has left a thick ice layer stretching from the Canadian islands to the northern coast of Russia.
The ice prevented dozens of yachts and a cruiser getting through America’s North-West Passage.
The shock memo surfaced just days before the Arctic freeze is about to begin and six years after warnings that global warming would melt the ice by this winter.
An ice-free Arctic was boldly predicted in a 2007 by Professor Wieslaw Maslowski, of the Naval Postgraduate School in Monterey, California.
He said his grim but conservative estimate was provided by the most realistic computer models. Cambridge University expert Professor Peter Wadhams added: “This is not a cycle, not just a fluctuation. In the end, it will all just melt away quite suddenly.”
On the back of the dire warnings, billions of pounds were invested in green measures to combat agents of climate change such as greenhouse gas emissions.
But the secret UN memo revealed that the ice has spread quickly following the smallest ever frozen surface area, this time last year.
It also shows how governments who fund the panel are terrified at the implications of the new predictions.