US space agency Nasa has announced it will send four astronauts to the Moon by the year 2020.
The project is set to cost £58bn ($104bn) and will use rocket technology already used on the space shuttle to cut the costs of developing a new ship.
"We will return to the Moon no later than 2020 and extend human presence across the Solar System and beyond," Dr Griffin said on Monday.
The last time people travelled to the Moon was 33 years ago.
On 20 July 1969 Neil Armstrong was the first man to walk on the Moon, when he travelled there on the Apollo 11.
Nasa continued to send manned crews to the Moon until 1972, and a total of 12 men walked on the lunar surface.
Experts said the new rocket would be "very Apollo-like, with updated technology. Think of it as Apollo on steroids."
One stop to Mars?
Artist's impression of the new lunar lander
Scientists now plan to use the Moon as a stop-off on a manned mission to Mars.
Unmanned American space crafts, including the Mars Reconnaissance Orbiter, are already exploring Mars.
But scientists are yet to send a person to the fiery planet.