Prof Hawking is in "no hurry to die"
He told the BBC that life could be wiped out by a nuclear disaster or asteroid hitting the planet.
But the Cambridge academic added: "Once we spread out into space and establish colonies our future should be safe."
Prof Hawking, 64, was speaking before receiving the UK's top science award, the Royal Society's Copley Medal.
He said there were no similar planets to earth in our solar system so man would "have to go to another star".
Prof Hawking said that current chemical and nuclear rockets were not adequate for taking colonists into space as they would mean a journey of 50,000 years.
He also discounted science-fiction ideas from programmes such as Star Trek, like using warp drive to travel at the speed of light, for taking mankind to a new outpost.
Instead he favoured "matter/anti-matter annihilation" as a means of propulsion.
He explained: "When matter and anti-matter meet up they disappear in a burst of radiation. If this was beamed out of the back of a spaceship it could drive it forward."
Travelling at just below the speed of light, it would mean a journey of about six years to reach a new star.
"It would take a lot of energy to accelerate to near the speed of light," he told BBC Radio 4's Today.
He became famous with the publication of his book A Brief History of Time in the late 1980s.
'Goal is space'
Prof Hawking was not given many years to live when he was diagnosed in the 1960s, aged 22, with motor neurone disease.
He said since then he had "learned not to look too far ahead, but to concentrate on the present".
"I am not afraid of death but in no hurry to die," he said.
"My next goal is to go into space, maybe Richard Branson will help me."
Sir Richard Branson's Virgin Group has contracted a firm to design and build a passenger spaceship.
Offshoot Virgin Galactic will own and operate at least five spaceships and two mother ships, and will charge £100,000 ($190,000) to carry passengers to an altitude of about 140km on a sub-orbital space flight.