The space object, which follows a similar path to our own around the Sun, will cross the Earth's orbit on Wednesday.
Astronomers say there is no danger of it hitting the planet because the Earth's gravity keeps it at bay.
"
There's no possibility that this asteroid could hit Earth
"
Don Yeomans, Nasa
The asteroid, known as 2002 AA29, will pass within 5.9 million kilometres (3.7 million miles) of the planet. This is the closest it has come for almost a century but is no near miss in astronomical terms.
The asteroid was spotted last year by an Air Force telescope used by the US space agency (Nasa) to track near-Earth objects.
The rock is about 60 metres (200 feet) across and has a very unusual orbit.
Sneaking up
The asteroid races around the Sun on a similar path to the Earth. Every now and again, the two change places, which is what will happen on Wednesday.
This time, the asteroid will close on Earth and gravity will force it into a lower, faster orbit.
It will then speed on ahead and should catch us up again in 95 years.
"There's no possibility that this asteroid could hit Earth, because Earth's gravity rebuffs its periodic advances and keeps it at bay," said Dr Don Yeomans of Nasa's Jet Propulsion Laboratory.
"The asteroid and Earth take turns sneaking up on each other, but they never get too close."
The object is too small to be easily seen from Earth. It is of great interest to astronomers, however.
They predict that its path will change in about 600 years but it will never become a true satellite like the Moon.